In triangle ABC, the measure of angle B is 70^ and the measure of angle C is 40^. The bisector of angle A intersects BC at point D. What is the measure of angle ADC?

SAT Lines, angles, and triangles Practice Question 13 (Hard)

Question bank / Lines, angles, and triangles

Math · Geometry and TrigonometryHard

In triangle $ABC$ , the measure of angle $B$ is $70^\circ$ and the measure of angle $C$ is $40^\circ$ . The bisector of angle $A$ intersects $\overline{BC}$ at point $D$ . What is the measure of angle $ADC$ ?

$105^\circ$

$35^\circ$

$75^\circ$

$110^\circ$

Show answer and explanation

Answer: A

Angle $A$ measures $180^\circ - 70^\circ - 40^\circ = 70^\circ$ , so the bisector creates two $35^\circ$ angles. In triangle $ADC$ , angle $DAC = 35^\circ$ and angle $C = 40^\circ$ . So angle $ADC = 180^\circ - 35^\circ - 40^\circ = 105^\circ$ .

Choice C is angle $ADB$ ( $180^\circ - 35^\circ - 70^\circ$ ), the angle on the other side of the bisector.

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