Question

The sum of two angles measures is 95 degrees. Angle 2 is 40 degrees smaller than 2 times angle 1. What are the measures of the two angles in degrees?

Answer 1

<1 = 45

<2 = 50

Explanation:

Let <1 = x

Let <2 = y

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x + y = 95

y = 2*x - 40

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I think the easiest way to do this is to substitute the second or bottom equation into the top equation. Substitute for y

x + 2x - 40 = 95 Combine like terms on the left.

3x - 40 = 95 Add 40 to both sides.

3x -40+40 = 95+40 Combine

3x = 135 Divide by 3

x = 45

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Now use the top equation to solve for y

x + y = 95

45 + y = 95 Subtract 45 from both sides.

45 - 45 + y = 95 -45 Combine

y = 50