Question

PQR and
GHK are supplementary angles. If
GHK is (2x - 8)
and
PQR is (4x + 2)
, what is the measure of
PQR?

Answer 1

Supplementary angles add up to 180°.
Given:
Angle 𝐺 𝐻 𝐾 = 2 𝑥 − 8 GHK=2x−8
Angle 𝑃 𝑄 𝑅 = 4 𝑥 + 2 PQR=4x+2
Since these angles are supplementary, we can set up the following equation:
( 2 𝑥 − 8 ) + ( 4 𝑥 + 2 ) = 180
Now, combine like terms: 6 𝑥 − 6 = 180
Add 6 to both sides:
6 𝑥 = 186
Now, divide both sides by 6: 𝑥 = 31
Now that we have the value of 𝑥 x, substitute it into the expression for 𝑃 𝑄 𝑅
PQR: 𝑃 𝑄 𝑅 = 4 𝑥 + 2 = 4 ( 31 ) + 2 = 124 + 2 = 126 °
So, the measure of angle 𝑃 𝑄 𝑅 PQR is 126°.