Answer:
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m<M = 27 degrees
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m<N = 29 degrees
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m<P = 124 degrees
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Explanation:
Triangle Sum Theorem
| All the interior angles in a triangle add up to equal 180 degrees. |
Using Triangle sum theorem, you can make an equation:
3x + (3x +2) + (14x - 2) = 180
Solve for x:
3x + 3x +2 + 14x - 2 = 180 (get rid of parentheses)
20x = 180 (add all like terms)
x = 9 (divide both sides by 20)
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Now you know that x = 9. You can use this to find the measure of all the angles by plugging in the value of x using the given expressions for each angle.
1. Find m<M:
m<M = 3x
x=9 so m<M = 3(9) = [27 degrees]
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2. Find m<N:
m<N = 3x + 2
x=9 so m<N = 3(9) + 2 = 27 + 2 = [29 degrees]
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3. Find m<P
m<P = 14x - 2
x = 9 so m<P = 14(9) - 2 = [124 degrees]
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Hope this helps!!