Question

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

Explanation:

Step1: Use the property of isosceles triangle

Since \( \triangle KLM\) has \(KL = KM\) (marked with the same tick - marks), it is an isosceles triangle. In an isosceles triangle, the base - angles are equal. The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(m\angle K+m\angle M + m\angle L=180^{\circ}\), and \(m\angle K = m\angle M\).
The equation is \(m\angle K + 56+(5y - 19)=180\). Let \(m\angle K=x\), then \(x + 56+(5y - 19)=180\). But since \(x = 56\) (because \(KL = KM\)), the equation for \(y\) (using the angle - sum property) is \(56+56+(5y - 19)=180\).

Step2: Solve for \(m\angle K\)

Since \(KL = KM\), by the property of isosceles triangles (equal sides have equal opposite angles), \(m\angle K=m\angle M\).

Answer:

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