If meaurement of angle DEF=(3x+5) degrees and measurement of angle KLM=(x+31) degrees, and goth angles are complementary to angle PQR, what are the measures of the angles?

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To find the measures of angles DEF and KLM, we're told that they are complementary to angle PQR.

Angles are considered complementary when the sum of their measures is equal to 90 degrees.

Therefore, we can write the equation:

(3x + 5) + (x + 31) = 90

Now, we can simplify the equation by combining like terms:

4x + 36 = 90

Next, let's isolate the variable by subtracting 36 from both sides of the equation:

4x = 90 - 36

Simplifying further:

4x = 54

Finally, divide both sides of the equation by 4 to solve for x:

x = 54 / 4
x = 13.5

Now that we have the value of x, we can substitute it back into the original equations to find the measures of DEF and KLM:

Measure of angle DEF = 3x + 5 = 3(13.5) + 5 = 40.5 + 5 = 45.5 degrees

Measure of angle KLM = x + 31 = 13.5 + 31 = 44.5 degrees

Therefore, angle DEF measures 45.5 degrees and angle KLM measures 44.5 degrees.