Determine the measures of ∠ L and ∠ M . The figure shows a triangle UpperWord LMN. Sides UpperWord MN and UpperWord LN of this triangle are produced to points Upper O and Upper P respectively. The angle UpperWord ONP is labeled as 48 degree, angle UpperWord NLM is labeled as x, and the angle UpperWord LMN is labeled as x.

Answers

Answer 1

Answer:

The measures of ∠ L and ∠ M are 180 degrees - x and 132 degrees - x, respectively.

Since the interior angles of a triangle add up to 180 degrees, we have the following equation:

x + x + L + M = 180 degrees

We also know that the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. Therefore, we have the following equation:

L = x + 48 degrees

We can substitute this equation into the first equation to get:

x + x + x + 48 degrees + M = 180 degrees

Combining like terms, we get:

3x + 48 degrees + M = 180 degrees

Subtracting 48 degrees from both sides, we get:

3x + M = 132 degrees

Subtracting x from both sides, we get:

2x + M = 132 degrees - x

We can now substitute this equation into the equation L = x + 48 degrees to get:

L = (132 degrees - x) + 48 degrees

L = 180 degrees - x

Therefore, the measures of ∠ L and ∠ M are 180 degrees - x and 132 degrees - x, respectively.

For such more question on degrees

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Answer 2

Answer:

Final answer:

In triangle LMN, both angle L and angle M are 24 degrees, calculated using the property of exterior angles in triangles.

Explanation:

From your question, it seems like we're dealing with an issue of triangle geometry and exterior angles in particular. In a triangle, the measure of an exterior angle is equal to the sum of the measures of the two non-adjacent interior angles. This means, in triangle LMN, angle ONP (which is 48 degrees) equals to the sum of angle NLM (which is x) and angle LMN (also x).

Therefore, we can make the equation as 2x = 48, where 2x accounts for angles NLM(x) and LMN(x). Solving this equation gives us x = 24. Hence, ∠L (or NLM) = 24 degrees and ∠M (or LMN) = 24 degrees.

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Answers

Answer:

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Answers

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