Question

11/7 - isosceles and equilateral practice
use the diagram to find the requested values:
what is the value of x?
what is the m∠a and the m∠c? degrees

Explanation:

Step1: Use the property of isosceles triangle

In an isosceles triangle, the base angles are equal. So, \(m\angle A=m\angle C = 2x^{\circ}\).

Step2: Apply the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(m\angle A + m\angle B+m\angle C=180^{\circ}\). Substitute \(m\angle A = 2x\), \(m\angle B = 50^{\circ}\), and \(m\angle C = 2x\) into the equation: \(2x+50 + 2x=180\).

Step3: Solve the equation for \(x\)

Combine like terms: \(4x+50 = 180\). Subtract \(50\) from both sides: \(4x=180 - 50=130\). Divide both sides by \(4\): \(x=\frac{130}{4}=32.5\).

Step4: Find \(m\angle A\) and \(m\angle C\)

Since \(m\angle A=m\angle C = 2x\), substitute \(x = 32.5\). Then \(m\angle A=m\angle C=2\times32.5 = 65^{\circ}\).

Answer:

The value of \(x\) is \(32.5\). The \(m\angle A\) and \(m\angle C\) are \(65\) degrees.