Question 9
First we are going to solve for Angle B. We should know that when two angles are on a straight line, they are supplementary, so they add to 180 degrees. We can use this to create an equation to solve for that angle.
6x + ∠B = 180
We can re-format this equation to isolate Angle B: ∠B = 180 -6x.
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Now, I will add the interior angles in the triangle. This is as all interior angles in a triangle must add up to 180 degrees.
(3x+10)+(x+40)+(180-6x) = 180
Simplify the expression: -2x + 230 = 180.
We will solve for x.
- -2x + 230 - 230 = 180 -230
- -2x = -50
- -2x ÷ -2 = -50 ÷ -2
- x = 25
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Now that we found x, we can now substitute x for each angle to see its measure in degrees.
Angle C
∠A = 3x + 10
= 3(25) + 10
= 75 + 10
= 85 degrees
Angle A
∠C = x + 40
= 25 + 40
= 65 degrees
Last Interior Angle
LIA = 180 -∠A - ∠C
= 180 - 85 - 65
= 30 degrees
Angle B: Exterior
∠B = 6x
= 6(25)
= 150 degrees
Hope this helps.