Question

find the following angle measures

m∠ead =

m∠cab =

Explanation:

Step1: Calculate \(m\angle EAD\)

Since \(\angle EAB = 90^{\circ}\) (right - angle) and \(\angle CAB = 61^{\circ}\), and \(\angle EAD+\angle CAD = 90^{\circ}\), and \(\angle CAD = 61^{\circ}\) (vertical angles are equal). Then \(m\angle EAD=90^{\circ}- 61^{\circ}\)

$$m\angle EAD = 29^{\circ}$$

Step2: Calculate \(m\angle CAB\)

\(\angle CAB\) and the angle of \(61^{\circ}\) are vertical angles. By the vertical - angles theorem (vertical angles are congruent), \(m\angle CAB = 180^{\circ}-90^{\circ}-61^{\circ}\)

$$m\angle CAB=119^{\circ}$$

Answer:

\(m\angle EAD = 29^{\circ}\), \(m\angle CAB = 119^{\circ}\)