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Angle Addition & Angle Bisectors — Easy Worksheet 2
Grade 10 · MathSheets Name: ____________________ Date: __________
Point D is in the interior of ∠ABC. Use the given information to answer each question.
How to solve
If D is in the interior of ∠ABC, then m∠ABD + m∠DBC = m∠ABC. If BD bisects ∠ABC, the two smaller angles are equal and each is half of m∠ABC. Set up the equation, solve for x, then substitute to find any angle that is asked for.
Example
m∠ABC = 78° and m∠ABD = 30°. Find m∠DBC.
Answer: 48°
Not quite. The answer is
💡 By the Angle Addition Postulate, m∠ABC = m∠ABD + m∠DBC = 43° + 64° = 107°.
✓ Correct!
Not quite. The answer is
💡 By the Angle Addition Postulate, m∠ABC = m∠ABD + m∠DBC = 43° + 64° = 107°.
💡 How to solve: Angle Addition & Angle Bisectors
If D is in the interior of ∠ABC, then m∠ABD + m∠DBC = m∠ABC. If BD bisects ∠ABC, the two smaller angles are equal and each is half of m∠ABC. Set up the equation, solve for x, then substitute to find any angle that is asked for.
Try a similar one
m∠ABD = 46° and m∠DBC = 27°. Find m∠ABC.
✓ 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
💡 A bisector splits ∠ABC into two equal halves, so m∠DBC = 102° ÷ 2 = 51°.
✓ Correct!
Not quite. The answer is
💡 A bisector splits ∠ABC into two equal halves, so m∠DBC = 102° ÷ 2 = 51°.
💡 How to solve: Angle Addition & Angle Bisectors
If D is in the interior of ∠ABC, then m∠ABD + m∠DBC = m∠ABC. If BD bisects ∠ABC, the two smaller angles are equal and each is half of m∠ABC. Set up the equation, solve for x, then substitute to find any angle that is asked for.
Try a similar one
m∠ABD = 15° and m∠DBC = 56°. Find m∠ABC.
✓ 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 Angle Addition Postulate, m∠ABC = m∠ABD + m∠DBC = 29° + 22° = 51°.
✓ Correct!
Not quite. The answer is
💡 By the Angle Addition Postulate, m∠ABC = m∠ABD + m∠DBC = 29° + 22° = 51°.
💡 How to solve: Angle Addition & Angle Bisectors
If D is in the interior of ∠ABC, then m∠ABD + m∠DBC = m∠ABC. If BD bisects ∠ABC, the two smaller angles are equal and each is half of m∠ABC. Set up the equation, solve for x, then substitute to find any angle that is asked for.
Try a similar one
m∠ABD = 32° and m∠DBC = 30°. Find m∠ABC.
✓ 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
💡 A bisector splits ∠ABC into two equal angles, so m∠DBC = m∠ABD = 34° and m∠ABC = 2 × 34° = 68°.
✓ Correct!
Not quite. The answer is
💡 A bisector splits ∠ABC into two equal angles, so m∠DBC = m∠ABD = 34° and m∠ABC = 2 × 34° = 68°.
💡 How to solve: Angle Addition & Angle Bisectors
If D is in the interior of ∠ABC, then m∠ABD + m∠DBC = m∠ABC. If BD bisects ∠ABC, the two smaller angles are equal and each is half of m∠ABC. Set up the equation, solve for x, then substitute to find any angle that is asked for.
Try a similar one
m∠ABC = 80° and m∠ABD = 32°. Find m∠DBC.
✓ 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 Angle Addition Postulate, m∠ABD + m∠DBC = m∠ABC, so m∠DBC = 107° − 32° = 75°.
✓ Correct!
Not quite. The answer is
💡 By the Angle Addition Postulate, m∠ABD + m∠DBC = m∠ABC, so m∠DBC = 107° − 32° = 75°.
💡 How to solve: Angle Addition & Angle Bisectors
If D is in the interior of ∠ABC, then m∠ABD + m∠DBC = m∠ABC. If BD bisects ∠ABC, the two smaller angles are equal and each is half of m∠ABC. Set up the equation, solve for x, then substitute to find any angle that is asked for.
Try a similar one
m∠ABC = 58° and m∠ABD = 18°. Find m∠DBC.
✓ 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
💡 A bisector splits ∠ABC into two equal angles, so m∠DBC = m∠ABD = 42° and m∠ABC = 2 × 42° = 84°.
✓ Correct!
Not quite. The answer is
💡 A bisector splits ∠ABC into two equal angles, so m∠DBC = m∠ABD = 42° and m∠ABC = 2 × 42° = 84°.
💡 How to solve: Angle Addition & Angle Bisectors
If D is in the interior of ∠ABC, then m∠ABD + m∠DBC = m∠ABC. If BD bisects ∠ABC, the two smaller angles are equal and each is half of m∠ABC. Set up the equation, solve for x, then substitute to find any angle that is asked for.
Try a similar one
m∠ABD = 28° and m∠DBC = 25°. Find m∠ABC.
✓ 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 Angle Addition Postulate, m∠ABD + m∠DBC = m∠ABC, so m∠DBC = 94° − 17° = 77°.
✓ Correct!
Not quite. The answer is
💡 By the Angle Addition Postulate, m∠ABD + m∠DBC = m∠ABC, so m∠DBC = 94° − 17° = 77°.
💡 How to solve: Angle Addition & Angle Bisectors
If D is in the interior of ∠ABC, then m∠ABD + m∠DBC = m∠ABC. If BD bisects ∠ABC, the two smaller angles are equal and each is half of m∠ABC. Set up the equation, solve for x, then substitute to find any angle that is asked for.
Try a similar one
m∠ABD = 25° and m∠DBC = 52°. Find m∠ABC.
✓ 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
💡 A bisector splits ∠ABC into two equal angles, so m∠DBC = m∠ABD = 46° and m∠ABC = 2 × 46° = 92°.
✓ Correct!
Not quite. The answer is
💡 A bisector splits ∠ABC into two equal angles, so m∠DBC = m∠ABD = 46° and m∠ABC = 2 × 46° = 92°.
💡 How to solve: Angle Addition & Angle Bisectors
If D is in the interior of ∠ABC, then m∠ABD + m∠DBC = m∠ABC. If BD bisects ∠ABC, the two smaller angles are equal and each is half of m∠ABC. Set up the equation, solve for x, then substitute to find any angle that is asked for.
Try a similar one
m∠ABD = 16° and m∠DBC = 40°. Find m∠ABC.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Angle Addition & Angle Bisectors — Easy Worksheet 2
Point D is in the interior of ∠ABC. Use the given information to answer each question.