Question

1. the diagram shows \\(\overleftrightarrow{mk}\\) intersecting \\(\overrightarrow{hj}\\) and \\(\overrightarrow{hl}\\) at point h.

which angle relationship is relevant?
complementary angle
part a
write an equation that can be used to solve for x.

part b
what is the measure of \\(\angle jhk\\)?

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. The angle \((2x + 47)^{\circ}\) and the angle composed of \(90^{\circ}\) and \((x - 32)^{\circ}\) are vertical angles. So, \(2x+47=90+(x - 32)\).

Step2: Solve the equation for \(x\)

$$
LATEXBLOCK0
$$

Step3: Find the measure of \(\angle JHK\)

We know that \(\angle JHK=y^{\circ}\), and from the right - angle relationship \(y+(x - 32)=90\). Substitute \(x = 11\) into the equation: \(y+(11 - 32)=90\), \(y-21 = 90\), \(y=90 + 21=111\)

Answer:

Part A: \(2x+47=90+(x - 32)\)
Part B: \(111\)