Question

1. ∠1 and ∠2 are vertical angles. if the measure of ∠2 is 105°, find the measure of ∠1.
2. ∠1 and ∠n are... measure of ∠1 is 42...
3. ∠7 and ∠q are supplementary angles. if the measure of ∠q is 64°, find the measure of ∠7.
4. ∠1 and... of ∠1 is 113°, fin...

Explanation:

Problem 6:

Step1: Recall vertical angles property

Vertical angles are equal, so \( m\angle1 = m\angle2 \).

Step2: Substitute given measure

Given \( m\angle2 = 105^\circ \), so \( m\angle1 = 105^\circ \).

Step1: Recall supplementary angles definition

Supplementary angles sum to \( 180^\circ \), so \( m\angle7 + m\angle Q = 180^\circ \).

Step2: Substitute \( m\angle Q = 64^\circ \)

\( m\angle7 + 64^\circ = 180^\circ \), then \( m\angle7 = 180^\circ - 64^\circ \).

Step3: Calculate the result

\( 180 - 64 = 116 \), so \( m\angle7 = 116^\circ \).

Answer:

\( 105^\circ \)

Problem 8: