Question

in the figure below, the measure of ∠4 = 90°, the measure of ∠5 = 61°, and the measure of ∠6 = 20°. what are the measures of ∠1, ∠2, and ∠3? m∠1 = □°

Explanation:

Step1: Use angle - sum property of a circle

The sum of angles around a point is 360°. Also, vertical angles are equal.

Step2: Find ∠1

We know that ∠4 = 90°, ∠5 = 61°, ∠6 = 20°. Since ∠1 and ∠5 are vertical angles, ∠1=∠5.
So, m∠1 = 61°.

Step3: Find ∠2

We know that ∠2+∠4+∠5+∠6 = 180° (a straight - line angle is 180°). Substitute the known values: ∠2+90° + 61°+20° = 180°. Then ∠2=180°-(90° + 61°+20°)=9°.

Step4: Find ∠3

Since ∠3 and ∠1 are vertical angles, ∠3 = ∠1 = 61°.

Answer:

m∠1 = 61°, m∠2 = 9°, m∠3 = 61°