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3 lines are shown. A line with points M, H, K intersects with a line with points J, H, L at point H. Another line extends from point H to point N in between angle K, H, J. Angle M H L is (3 x 20) degrees, angle K H N is (x 25) degrees, and angle J H N is (x 20) degrees. What is the measure of AngleJHN? 25° 45° 50° 95°.

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MrRoyal

The three lines form vertical angles, such that the measure of angle JHN is 45 degrees

The angles are given as:

[tex]\angle MHL = 3x + 20[/tex]

[tex]\angle KHN = x + 25[/tex]

[tex]\angle JHN = x + 20[/tex]

Such that:

[tex]\angle MHL = \angle JHN + \angle KHN[/tex] ---- by the theorem of vertical angles (see attachment)

So, we have:

[tex]3x + 20 = x + 20 + x +25[/tex]

Collect like terms

[tex]3x - x -x= 20-20+25[/tex]

[tex]x = 25[/tex]

Substitute 25 for x in [tex]\angle JHN = x + 20[/tex]

This gives

[tex]\angle JHN = 25 + 20[/tex]

[tex]\angle JHN = 45[/tex]

Hence, the measure of angle JHN is 45 degrees

Read more about vertical angles at:

https://brainly.com/question/1673457

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