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Isosceles & Equilateral Triangles — Easy Worksheet 2
Grade 10 · MathSheets Name: ____________________ Date: __________
Tick marks show congruent sides. Use the diagram and the given information to answer each question.
How to solve
In an isosceles triangle the angles opposite the congruent sides (the base angles) are equal, so vertex angle + 2 × base angle = 180°. An equilateral triangle has three equal sides and three 60° angles. Set equal parts equal to each other (or to 60°), solve for x, and substitute if needed.
Example
△ABC is isosceles with AB = AC and m∠A = 92°. Find m∠B.
Answer: 44°
Not quite. The answer is
💡 By the Base Angles Theorem, AB = AC means m∠B = m∠C. The angles of a triangle add to 180°, so 2 × m∠B = 180° − 98° = 82°. Divide by 2: m∠B = 82° ÷ 2 = 41°.
✓ Correct!
Not quite. The answer is
💡 By the Base Angles Theorem, AB = AC means m∠B = m∠C. The angles of a triangle add to 180°, so 2 × m∠B = 180° − 98° = 82°. Divide by 2: m∠B = 82° ÷ 2 = 41°.
💡 How to solve: Isosceles & Equilateral Triangles
In an isosceles triangle the angles opposite the congruent sides (the base angles) are equal, so vertex angle + 2 × base angle = 180°. An equilateral triangle has three equal sides and three 60° angles. Set equal parts equal to each other (or to 60°), solve for x, and substitute if needed.
Try a similar one
△ABC is isosceles with AB = AC and m∠A = 30°. Find m∠B.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 By the Base Angles Theorem, m∠C = m∠B = 75°. The angles of a triangle add to 180°, so m∠A = 180° − 2 × 75° = 180° − 150° = 30°.
✓ Correct!
Not quite. The answer is
💡 By the Base Angles Theorem, m∠C = m∠B = 75°. The angles of a triangle add to 180°, so m∠A = 180° − 2 × 75° = 180° − 150° = 30°.
💡 How to solve: Isosceles & Equilateral Triangles
In an isosceles triangle the angles opposite the congruent sides (the base angles) are equal, so vertex angle + 2 × base angle = 180°. An equilateral triangle has three equal sides and three 60° angles. Set equal parts equal to each other (or to 60°), solve for x, and substitute if needed.
Try a similar one
△ABC is isosceles with AB = AC and m∠A = 108°. Find m∠B.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 An equilateral triangle is also equiangular, and its three angles add to 180°. So m∠C = 180° ÷ 3 = 60°.
✓ Correct!
Not quite. The answer is
💡 An equilateral triangle is also equiangular, and its three angles add to 180°. So m∠C = 180° ÷ 3 = 60°.
💡 How to solve: Isosceles & Equilateral Triangles
In an isosceles triangle the angles opposite the congruent sides (the base angles) are equal, so vertex angle + 2 × base angle = 180°. An equilateral triangle has three equal sides and three 60° angles. Set equal parts equal to each other (or to 60°), solve for x, and substitute if needed.
Try a similar one
△ABC is isosceles with AB = AC and m∠A = 130°. Find m∠B.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 By the Base Angles Theorem, AB = AC means m∠B = m∠C. The angles of a triangle add to 180°, so 2 × m∠B = 180° − 96° = 84°. Divide by 2: m∠B = 84° ÷ 2 = 42°.
✓ Correct!
Not quite. The answer is
💡 By the Base Angles Theorem, AB = AC means m∠B = m∠C. The angles of a triangle add to 180°, so 2 × m∠B = 180° − 96° = 84°. Divide by 2: m∠B = 84° ÷ 2 = 42°.
💡 How to solve: Isosceles & Equilateral Triangles
In an isosceles triangle the angles opposite the congruent sides (the base angles) are equal, so vertex angle + 2 × base angle = 180°. An equilateral triangle has three equal sides and three 60° angles. Set equal parts equal to each other (or to 60°), solve for x, and substitute if needed.
Try a similar one
△ABC is isosceles with AB = AC and m∠A = 40°. Find m∠B.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 By the Base Angles Theorem, m∠C = m∠B = 42°. The angles of a triangle add to 180°, so m∠A = 180° − 2 × 42° = 180° − 84° = 96°.
✓ Correct!
Not quite. The answer is
💡 By the Base Angles Theorem, m∠C = m∠B = 42°. The angles of a triangle add to 180°, so m∠A = 180° − 2 × 42° = 180° − 84° = 96°.
💡 How to solve: Isosceles & Equilateral Triangles
In an isosceles triangle the angles opposite the congruent sides (the base angles) are equal, so vertex angle + 2 × base angle = 180°. An equilateral triangle has three equal sides and three 60° angles. Set equal parts equal to each other (or to 60°), solve for x, and substitute if needed.
Try a similar one
△ABC is isosceles with AB = AC and m∠A = 28°. Find m∠B.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 By the Base Angles Theorem, AB = AC means m∠B = m∠C. The angles of a triangle add to 180°, so 2 × m∠B = 180° − 114° = 66°. Divide by 2: m∠B = 66° ÷ 2 = 33°.
✓ Correct!
Not quite. The answer is
💡 By the Base Angles Theorem, AB = AC means m∠B = m∠C. The angles of a triangle add to 180°, so 2 × m∠B = 180° − 114° = 66°. Divide by 2: m∠B = 66° ÷ 2 = 33°.
💡 How to solve: Isosceles & Equilateral Triangles
In an isosceles triangle the angles opposite the congruent sides (the base angles) are equal, so vertex angle + 2 × base angle = 180°. An equilateral triangle has three equal sides and three 60° angles. Set equal parts equal to each other (or to 60°), solve for x, and substitute if needed.
Try a similar one
△ABC is isosceles with AB = AC and m∠A = 92°. Find m∠B.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 All three sides of an equilateral triangle are congruent, so BC = AB = 24.
✓ Correct!
Not quite. The answer is
💡 All three sides of an equilateral triangle are congruent, so BC = AB = 24.
💡 How to solve: Isosceles & Equilateral Triangles
In an isosceles triangle the angles opposite the congruent sides (the base angles) are equal, so vertex angle + 2 × base angle = 180°. An equilateral triangle has three equal sides and three 60° angles. Set equal parts equal to each other (or to 60°), solve for x, and substitute if needed.
Try a similar one
△ABC is isosceles with AB = AC and m∠A = 76°. Find m∠B.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 By the Base Angles Theorem, m∠C = m∠B = 38°. The angles of a triangle add to 180°, so m∠A = 180° − 2 × 38° = 180° − 76° = 104°.
✓ Correct!
Not quite. The answer is
💡 By the Base Angles Theorem, m∠C = m∠B = 38°. The angles of a triangle add to 180°, so m∠A = 180° − 2 × 38° = 180° − 76° = 104°.
💡 How to solve: Isosceles & Equilateral Triangles
In an isosceles triangle the angles opposite the congruent sides (the base angles) are equal, so vertex angle + 2 × base angle = 180°. An equilateral triangle has three equal sides and three 60° angles. Set equal parts equal to each other (or to 60°), solve for x, and substitute if needed.
Try a similar one
△ABC is isosceles with AB = AC and m∠A = 40°. Find m∠B.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Isosceles & Equilateral Triangles — Easy Worksheet 2
Tick marks show congruent sides. Use the diagram and the given information to answer each question.