Question

what is the measure of ∠k?

m∠k =

6 7 8 9 10 11 12 13 14 15

Explanation:

Step1: Recognize the triangle type

Since \(KL = KM\), \(\triangle KLM\) is an isosceles triangle. In an isosceles triangle, the base - angles are equal. Let \(\angle K=\angle L\).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(\angle K+\angle L+\angle M = 180^{\circ}\). Since \(\angle K=\angle L=(5y - 19)^{\circ}\) and \(\angle M = 56^{\circ}\), we have \((5y-19)+(5y - 19)+56=180\).
First, simplify the left - hand side: \(10y-38 + 56=180\), which becomes \(10y+18=180\).
Subtract 18 from both sides: \(10y=180 - 18=162\).
Divide both sides by 10: \(y=\frac{162}{10}=16.2\).
Then \(\angle K=(5y - 19)^{\circ}\). Substitute \(y = 16.2\) into the formula: \(5\times16.2-19=81 - 19=62^{\circ}\).

Answer:

\(62\)