Question

4 - 2 angles of triangles practice
find the measure of each numbered angle
m∠1 = degrees
m∠2 = degrees

Explanation:

Step1: Find \(m\angle1\)

In \(\triangle BCD\), we know that the sum of angles in a triangle is \(180^{\circ}\). Since \(\angle BDC = 90^{\circ}\) and \(\angle C=64^{\circ}\), then \(m\angle1=180^{\circ}-90^{\circ}-64^{\circ}\)

$$m\angle1 = 26^{\circ}$$

Step2: Find \(m\angle2\)

In \(\triangle ABD\), \(\angle A = 90^{\circ}\), and we know that \(\angle ABD=58^{\circ}\). Using the angle - sum property of a triangle (\(\angle A+\angle ABD+\angle2 = 180^{\circ}\)), we substitute the values: \(90^{\circ}+58^{\circ}+\angle2=180^{\circ}\). Then \(\angle2=180^{\circ}-90^{\circ}-58^{\circ}\)

$$m\angle2 = 32^{\circ}$$

Answer:

\(m\angle1 = 26\) degrees, \(m\angle2=32\) degrees