Question

consider the triangle to the right. a. write an equation that can be used to find the value of y. b. what is m∠k? a. write the equation below. (do not simplify. do not combine like terms.)

Explanation:

Step1: Recall angle - sum property of isosceles triangle

In an isosceles triangle, if \(MK = KL\), then \(\angle M=\angle L\). The sum of interior angles of a triangle is \(180^{\circ}\). So the equation to find \(y\) is \(56+(5y - 19)+(5y - 19)=180\).

Step2: Recall property of isosceles - triangle angles

Since \(MK = KL\), \(\angle K=180 - 2\angle L\). First, simplify the sum - of - angles equation \(56+(5y - 19)+(5y - 19)=180\) to \(56 + 10y-38 = 180\), then \(10y+18 = 180\), and \(10y=162\), \(y = 16.2\). Then \(\angle L=5y - 19=5\times16.2-19=81 - 19 = 62^{\circ}\). So \(m\angle K=180-2\times62=180 - 124 = 56^{\circ}\).

Answer:

a. \(56+(5y - 19)+(5y - 19)=180\)
b. \(56^{\circ}\)