Question

You are given that angle GHJ is a complement of angle RST and angle RST is a supplement of angle ABC. Let the measurement of angle GHJ be x°. What is the measure of angle ABC?

Answer 1

GHJ = x

GHJ (or x) is a compliment of RST....complimentary angles, when added = 90...so RST = (90 - x)

RST is a supplement of ABC....supplementary angles, when added = 180...so ABC = (180 - RST)...and remember RST = (90 - x)

so ABC = 180 - (90 - x)
= 180 - 90 + x
= 90 + x....or 90 + GHJ <===

Answer 2

the measure of ∠ABC = (90 + x)°

Explanation:

It has been given that ∠GHJ is complementary angle of ∠RST.

So ∠GHJ + ∠RST = 90°-----------(1)

∠RST is a supplement of ∠ABC.

Then ∠ABC + ∠RST = 180° ---------(2)

If ∠GHJ = x° then we have to find the measure of ∠ABC.

By subtraction equation (1) from (2)

(∠ABC + ∠RST) - (∠GHJ + ∠RST) = 180 - 90

∠ABC - ∠GHJ = 90°

Now we put ∠GHJ = x°

∠ABC - x = 90°

∠ABC = (90 + x)°

Therefore, the measure of ∠ABC = (90 + x)°