Question

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

part a
write an equation that can be used to solve for ( x ).

part b
what is the measure of ( angle mhl )?

Explanation:

Part A

Step1: Use the angle - sum property of a right - angle

Since \( \angle LHJ = 90^{\circ}\), and the sum of angles around a point on a straight line (here related to the angles \(x + 54\), \(x-10\) and the right - angle) gives the equation.
The sum of angles \( (x + 54)+90+(x - 10)=180\) (because the sum of angles on a straight line is \(180^{\circ}\)).

Part B

Step1: Solve the equation for \(x\)

First, simplify the equation from Part A:

$$
LATEXBLOCK0
$$

Step2: Find the measure of \(y\)

We know that \(y+(x + 54)=180\) (linear - pair of angles). Substitute \(x = 23\) into the equation:
\(y+(23 + 54)=180\), so \(y+77 = 180\), then \(y=103\)

Answer:

Part A

The equation is \((x + 54)+90+(x - 10)=180\)

Part B

The measure of \(\angle MHL\) is \(103^{\circ}\)