Question

△abc is an isosceles triangle, where \overline{ab} \cong \overline{ac}.
the measure of \angle a is 118°. what are the measures of the missing angles?
m\angle b

Explanation:

Step1: Recall the property of isosceles triangle

In an isosceles triangle \(\triangle ABC\) with \(\overline{AB}\cong\overline{AC}\), \(\angle B=\angle C\).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle B = m\angle C=x\). Then \(m\angle A+m\angle B + m\angle C=180^{\circ}\).
Substitute \(m\angle A = 118^{\circ}\) into the equation: \(118^{\circ}+x + x=180^{\circ}\).

Step3: Solve the equation for \(x\)

Combine like terms: \(118^{\circ}+2x=180^{\circ}\).
Subtract \(118^{\circ}\) from both sides: \(2x=180^{\circ}- 118^{\circ}=62^{\circ}\).
Divide both sides by \(2\): \(x=\frac{62^{\circ}}{2}=31^{\circ}\).

Answer:

\(m\angle B = 31^{\circ}\)