Question

assessment: 25 - 26_hisd_cadfa_g7_mth_e_11.21

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 in terms of \(x\)

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

Step2: Use triangle - angle sum property

The sum of angles in a triangle is \(180^{\circ}\). So \(\angle M+\angle N+\angle P = 180^{\circ}\). Substitute the expressions: \((x + 10)+(2x+20)+(2x + 20)=180\)

Step3: Simplify the equation

Combine like terms: \(x+10+2x + 20+2x+20=180\), which gives \(5x+50 = 180\)

Step4: Solve for \(x\)

Subtract \(50\) from both sides: \(5x=180 - 50=130\). Then divide by \(5\): \(x=\frac{130}{5}=26\)

Answer:

D. 26