Question

nc math 2 (1st summative test)
name: bianca
date: october 01, 2025
i. choose the best answer.

1. in the following figure of two intersecting lines, what is the measure of ∠2?
2. what is the value of x, shown below?

use the following diagram of parallel lines cut by a transversal to answer questions 3 through

1. what is the measure of ∠8?
2. what is the measure of ∠3?
3. what is the measure of ∠6?

Explanation:

Step1: Identify vertical - angle property for question 1

Vertical angles are equal. The angle opposite to ∠2 is 142°. So ∠2 = 142°.

Step2: Use linear - pair property for question 2

A linear pair of angles sums to 180°. So 60+(5x - 10)=180. First simplify: 5x+50 = 180, then 5x=180 - 50 = 130, and x = 26.

Step3: Use corresponding - angles and linear - pair for question 3

Corresponding angles are equal. The angle corresponding to 5x + 35 is 45° (alternate - exterior to the given 45° angle). So 5x+35 = 45, 5x=10, x = 2. ∠8 and the 45° angle are supplementary. So ∠8=180 - 45=135°.

Step4: Use vertical - angle property for question 4

∠3 and ∠8 are vertical angles. Since ∠8 = 135°, ∠3 = 135°.

Step5: Use vertical - angle property for question 5

∠6 and the angle corresponding to 5x + 35 are vertical angles. Since the corresponding angle to 5x + 35 is 45°, ∠6 = 45°.

Answer:

1. D. 142°
2. B. 26°
3. D. 135°
4. C. 135°
5. A. 45°