Question

1. the measures of the angles of a triangle are given.

a. the measure of angle ( m ) is ( (x + 10)^{circ} ).
b. the measure of angle ( n ) is twice the measure of angle ( m ).
c. the measure of angle ( p ) is equal to the measure of angle ( n ).
what is the value of ( x )?
a. 10
b. 15
c. 20
d. 26

Explanation:

Step1: Express angles N and P in terms of x

Given angle \(M=(x + 10)^{\circ}\). Since angle \(N\) is twice angle \(M\), then \(N = 2(x+10)^{\circ}=(2x + 20)^{\circ}\). And since angle \(P\) is equal to angle \(N\), then \(P=(2x + 20)^{\circ}\).

Step2: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So \(M+N + P=180^{\circ}\). Substitute the expressions for \(M\), \(N\), and \(P\):
\((x + 10)+(2x + 20)+(2x + 20)=180\)
Combine like terms:
\(x+2x+2x+10 + 20+20=180\)
\(5x+50 = 180\)
Subtract 50 from both sides:
\(5x=180 - 50\)
\(5x=130\)
Divide both sides by 5:
\(x=\frac{130}{5}=26\)

Answer:

D. 26