Question

in the triangle below, \\( \angle k \\) is a right angle. suppose that \\( m \angle l=(5 x) \\) and \\( m \angle m=(2 x+34) \\).
(a) write an equation to find \\( x \\). make sure you use an \=\ sign in your answer.
equation: \\( 5 x+(2 x+34)+90+180 \\)

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). In \(\triangle KLM\), \(\angle K = 90^{\circ}\), \(\angle L=(5x)^{\circ}\), and \(\angle M=(2x + 34)^{\circ}\).
So, \(m\angle K+m\angle L+m\angle M = 180^{\circ}\).
Substitute the given angle measures: \(5x+(2x + 34)+90=180\).

Answer:

\(5x+(2x + 34)+90 = 180\)