Question

Some angles are shown. Complete each of the 2 activities for this Task. Activity 1 of 2 The measure of angle NOP is 140°. Which of these equations could be used to find the measure of angle NOQ? A. 23+x=140 B. x−23=140 C. 23×x=140 D. 140÷23=x Activity 2 of 2 What is the measure, in degrees, of angle NOQ?

Answer 1

Answer:

A. 23+x=140

Step-by-step explanation:

The angle addition postulate states that the measure of a larger angle formed by two or more smaller angles placed side by side is the the sum of the smaller angles. The angle addition postulate states that if B is in the interior of AOC , then:

m∠AOB + m∠BOC = m∠AOC.

From the image:

∠NOP = ∠NOQ + ∠QOP

∠NOP = 140, ∠NOQ = x, ∠QOP = 23

substituting:

140 = x + 23

x = 140 - 23 = 117

∠NOQ = 117°