Finding Unknown Angle Measures of Intersecting Lines

Published on August 21, 2026

Geometry

Learn how to find the unknown angle measure m∠MHJ created by intersecting lines using vertical and supplementary angle properties.

Question

answer

Answer

To find the measure of the unknown angle

, we can use the geometric properties of intersecting lines shown in the figure.

1. Analyze the given information

The figure shows two lines,

and

, intersecting at point

. This intersection creates four angles around point

.
From the image, we have the following known angle measures:

(This is given in the text box as a completed step)
(This is given in the text box as a completed step)

2. Identify the relationship for

The angle we need to find is

. There are two main ways to solve this:

Method A: Using Vertical Angles
Vertical angles are the angles opposite each other when two lines intersect. They are always equal.

and are vertical angles.
Therefore, .
Since , then .

Method B: Using Supplementary Angles (Linear Pairs)
Angles that lie on a straight line and share a common side are supplementary, meaning their sum is

and lie on the straight line .
Therefore, .
.
.

Alternatively,

and

lie on the straight line

Final Answer:

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