Question

A and B are complementary to each other. If m∠A = 26° + x and m∠B = 38° + x, what is the value of x?

A.13°
B.14°
C.58°
D.18°

Please don't reply just for the points, I really need help understanding these things, if possible please leave me an explanation on how you got this. P.S Complementary angles add up to 90 degrees

Answer 1

A. 13

Step-by-step explanation:

What we are given....

∠A = 26° + x

∠B = 38° + x

∠A and ∠B are complementary

If complementary angles add up to equal 90° and ∠A and ∠B are complementary to each other

Then 26 + x + 38 + x = 90

^ ( Note that we just created an equation that we can use to solve for x )

Now its just basic algebra

26 + x + 38 + x = 90

step 1 combine like terms

26 + 38 = 64

x + x = 2x

we now have 64 + 2x = 90

step 2 subtract 64 from each side

64 - 64 cancels out

90 - 64 = 26

we now have 26 = 2x

step 3 divide each side by 2

26 / 2 = 13

2x / 2 = x

we're left with x = 13