Question

given:
aj⊥ax.
ad bisects ∠gax.
m∠jar = 20°.
enter the measures and reasons to justi needed to calculate m∠gad.
m∠gad =
diagram notes:

Explanation:

Step1: Find \(m\angle JAX\)

Since \(\overline{AJ}\perp\overline{AX}\), \(m\angle JAX = 90^{\circ}\). Given \(m\angle JAR=20^{\circ}\), then \(m\angle GAX=180^{\circ}-m\angle JAR - m\angle JAX\).

$$m\angle GAX=180 - 20-90=70^{\circ}$$

Step2: Use the angle - bisector property

Since \(\overline{AD}\) bisects \(\angle GAX\), by the definition of an angle bisector (\(AD\) divides \(\angle GAX\) into two equal angles), if \(m\angle GAX = 70^{\circ}\), then \(m\angle GAD=\frac{1}{2}m\angle GAX\).

$$m\angle GAD=\frac{70}{2}=35^{\circ}$$

Answer:

\(35\)