Question

1. m∠prs =
2. the length of the base of an isosceles triangle is 2x. the length of one leg is 4x - 20. the perimeter of the triangle is 40. what is the value of x?

Explanation:

Step1: Use the property of isosceles triangle

In an isosceles triangle, the two legs are equal. The perimeter of a triangle is the sum of all its sides. Let the base be \(b = 2x\) and each leg be \(l=4x - 20\). The perimeter \(P=b + 2l\).

Step2: Substitute into the perimeter formula

Given \(P = 40\), we substitute into the formula \(40=2x+2(4x - 20)\).
First, expand the right - hand side: \(40=2x + 8x-40\).

Step3: Combine like terms

Combine the \(x\) terms: \(40=(2x + 8x)-40\), so \(40 = 10x-40\).

Step4: Solve for \(x\)

Add \(40\) to both sides: \(40 + 40=10x-40 + 40\), which gives \(80 = 10x\).
Divide both sides by \(10\): \(x=\frac{80}{10}=8\).

Answer:

\(8\)