Question

the measure of \\( \angle c \\) is \\( 45 ^ { \circ } \\). what are the measures of the missing angles?\\( m \angle a \\)\\( m \angle a = 90 \\)\\( m \angle b \\)

Explanation:

Step1: Use the property of isosceles triangle

Since the two sides of the triangle are equal (marked with the same symbol), the triangle is isosceles. In an isosceles triangle, the base angles are equal. So, if \(m\angle C = 45^{\circ}\), then \(m\angle B=m\angle C\) (base - angles of isosceles triangle).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle A=x\), \(m\angle B = 45^{\circ}\), \(m\angle C=45^{\circ}\). Then \(x + 45^{\circ}+45^{\circ}=180^{\circ}\).

$$x=180^{\circ}-(45^{\circ} + 45^{\circ})$$

$$x = 90^{\circ}$$

Answer:

\(m\angle A = 90^{\circ}\), \(m\angle B=45^{\circ}\)