Question

1. the measure of ∠1 is 95°. which of the following is not a true statement about the angles shown below?

a. the measure of ∠3 is 95°.

b. the measure of ∠4 is 105°.

c. the measure of ∠2 is 85°.

d. ∠2 and ∠4 are vertical angles.

Explanation:

Step1: Recall angle properties (vertical, supplementary)

Vertical angles are equal, supplementary angles sum to \(180^\circ\). Given \(\angle1 = 95^\circ\).

Step2: Analyze Option A

\(\angle1\) and \(\angle3\) are vertical angles, so \(\angle3=\angle1 = 95^\circ\). A is true.

Step3: Analyze Option B

\(\angle1\) and \(\angle4\) are supplementary (linear pair), so \(\angle4 = 180^\circ - 95^\circ= 85^\circ\), not \(105^\circ\). B is false.

Step4: Analyze Option C

\(\angle1\) and \(\angle2\) are supplementary, so \(\angle2 = 180^\circ - 95^\circ = 85^\circ\). C is true.

Step5: Analyze Option D

\(\angle2\) and \(\angle4\) are vertical angles (opposite angles when lines intersect), so D is true.

Answer:

B. The measure of \(\angle4\) is \(105^\circ\)