Question

the measures of the angles of a triangle are shown in the figure below. solve for x.

Explanation:

Step1: Recall angle - sum property

The sum of the interior angles of a triangle is 180°. Let the other two angles be \(x\) and \(x\) (assuming the triangle is isosceles as no other angle measures are given and we need to solve for \(x\)). So, \(x + x+40^{\circ}=180^{\circ}\).

Step2: Combine like - terms

Combining the \(x\) terms, we get \(2x + 40^{\circ}=180^{\circ}\).

Step3: Isolate the variable term

Subtract \(40^{\circ}\) from both sides: \(2x=180^{\circ}- 40^{\circ}\), so \(2x = 140^{\circ}\).

Step4: Solve for \(x\)

Divide both sides by 2: \(x=\frac{140^{\circ}}{2}=70^{\circ}\).

Answer:

\(70^{\circ}\)