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.
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In triangle LMN, both angle L and angle M are 24 degrees, calculated using the property of exterior angles in triangles.
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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14.6 feet long would the cloth have to be so that the opening of the tent was 6 feet high and 8 feet wide.
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
To find the length of the cloth needed to make the tent, we can use the Pythagorean theorem.
The triangle formed by the tent is isosceles, the hypotenuse is equal to one of the equal sides, and we can use the Pythagorean theorem to solve for "x".
The length of the hypotenuse is:
√(1/2× 8)² + 6² )
√16 + 36 )
√52= 2√13
Since the tent is isosceles, the length of each of the two equal sides of the triangle is also "x", so we have:
2x = 2√13
Solving for "x", we get:
x = √13
Therefore, the length of the cloth needed to make the tent is:
2x + 8
= 2√13 + 8
= 14.61 feet
So the cloth would have to be 14.61 feet long.
Hence, 14.6 feet long would the cloth have to be so that the opening of the tent was 6 feet high and 8 feet wide.
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Answer:
7π/6.
Step-by-step explanation:
The range in the third quadrant is π to 3π/2 ( or π to 1.5π) so its not π/3 or 3π/4.
5π/3 = 1.67π so it's not this one.
7π/6 = 1.167π so it's this one.
Answer:
m=-3
Step-by-step explanation:
m-10=-13
m=-13+10
m=-3
Answer:
m = -3
Step-by-step explanation:
Translate into an expression a part of the expression at a time.
ten less than m is -13
m - 10
ten less than m is -13
m - 10 = -13
Add 10 to both sides.
m = -3