Geometry and TrigonometryHardAngle formed by an angle bisector
Geometry and Trigonometry practice question
In triangle ABC, angle A measures 50° and angle B measures 60°. The bisector of angle C meets side AB at point D. What is the measure, in degrees, of angle ADC?
Answer: 95
Angle C = 180 − 50 − 60 = 70°, so the bisector splits it into two 35° angles. In triangle ADC the angles are 50° (at A), 35° (at C) and angle ADC = 180 − 50 − 35 = 95°.
Common wrong answers
- If you answered 35
- 35 is half of angle C, the angle at C inside triangle ADC — not the angle at D.
- If you answered 70
- 70 is angle C before it is bisected.
- If you answered 85
- 85 is angle BDC, the angle on the OTHER side of D: 180 − 60 − 35. Angle ADC is in triangle ADC, with the 50° angle at A.
More Geometry and Trigonometry questions
- Hard
In a right triangle, one leg is 5 and the hypotenuse is 13. What is the length of the other leg? - Hard
A circle has a radius of 4. What is the length of an arc that subtends a central angle of 90°? - Hard
A circle is defined by the equation (x − 3)² + (y + 2)² = 25. What is the radius of the circle? - Hard
What is 135° expressed in radians? - Hard
What is the length of segment PT? - Hard
What is the measure, in degrees, of the central angle of this sector?
Not affiliated with the College Board. SAT is a trademark of the College Board.