Question

for the two problems below, apply what you know about isosceles triangles to solve for x (and find the measure of angle m in number 6)

Explanation:

Step1: Use the property of isosceles triangle

In an isosceles triangle, the base - angles are equal. So, \(2x=x + 30\).

Step2: Solve the equation

Subtract \(x\) from both sides of the equation \(2x=x + 30\). We get \(2x-x=x + 30-x\), which simplifies to \(x = 30\).

Step3: Find the measure of \(\angle M\)

Since \(\angle M\) and \(2x\) are supplementary (they form a linear - pair), \(\angle M=180^{\circ}-2x\). Substitute \(x = 30\) into the equation. Then \(2x=2\times30 = 60\), and \(\angle M=180 - 60=120^{\circ}\).

Answer:

\(120^{\circ}\)