Question

1. what is the measure of angle k?

a) 56
b) 136
c) 44
d) 132

Explanation:

Step1: Identify the triangle type

Since two sides of the triangle are equal (marked with same tick marks), it is an isosceles triangle. In an isosceles triangle, the base - angles are equal. So, \(\angle Y=\angle Z = 44^{\circ}\).

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let \(\angle K\) be \(x\). Then \(x + 44^{\circ}+44^{\circ}=180^{\circ}\).

$$x=180^{\circ}-(44^{\circ} + 44^{\circ})$$

$$x = 180^{\circ}-88^{\circ}$$

$$x = 92^{\circ}$$

Answer:

A. \(92^{\circ}\)