Question

the measures of a triangle are as follows. -the measure of angle a is (x + 7). -the measure of angle b is 3 times the measure of angle a. -the measure of angle c is the same as angle a. what is x? a) 11 b) 43 c) 29 d) 90

Explanation:

Step1: Express angles in terms of \(x\)

Angle \(a=(x + 7)\), angle \(b = 3(x + 7)=3x+21\), angle \(c=(x + 7)\)

Step2: Use triangle - angle sum property

Since the sum of angles in a triangle is \(180^{\circ}\), we have \((x + 7)+(3x + 21)+(x + 7)=180\)
Combine like terms: \(x+3x+x+7 + 21+7=180\), so \(5x+35 = 180\)

Step3: Solve for \(x\)

Subtract \(35\) from both sides: \(5x=180 - 35=145\)
Divide both sides by \(5\): \(x=\frac{145}{5}=29\)

Answer:

C. 29