Measure of ∠M is 52° and measure of ∠LNM is 38°
Step-by-step explanation:
From the attached figure the given is:
1. Line LP intersects line OM at point N
2. m∠PNM is 142°
3. m∠L is 90°
We need to find m∠M and m∠LNM
∵ Line LP intersects line OM at point N
∴ m∠PNM + m∠LNM = 180° ⇒ pair of linear angles
∵ m∠PNM = 142°
∴ 142 + m∠LNM = 180
- Subtract 142 from both sides
∴ m∠LNM = 38°
In ΔNLM
∵ m∠LNM + m∠L + m∠M = 180° ⇒ interior angles of a triangle
∵ m∠LNM = 38° ⇒ proved
∵ m∠L = 90° ⇒ given
∴ 38 + 90 + m∠M = 180
- Add like terms in the left hand side
∴ 128 + m∠M = 180
- Subtract 128 from both sides
∴ m∠M = 52°
Measure of ∠M is 52° and measure of ∠LNM is 38°
Learn more:
You can learn more about angles in brainly.com/question/1599887
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