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4 years ago

Compute the missing angles in the given figure.

Mathematics

1 answer:

anyanavicka [17]4 years ago

7 0

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

#LearnwithBrainly

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