Question

PLS HELP 99 POINTS! GEOMETRY & ALGEBRA QUESTION

find m
a-52
b-142
c-24
d-50
e-64

Answer 1

hey!! So let’s start off by knowing that we have to sue the exterior angel theorem- which states that the two remote angles of a triangle (the ones that are NOT next to the exterior angle) will add up to equal the exterior angles measure.

Since we know that a right angle (Q) is 90 degrees we can use it to add to (x+2) to get the exterior angles measure.

So our equation would be X+2+90= 3x-8

Then : X+92=3x-8
X+100 =3x
100= 2x
50 = x
BUT THATS NOT OUR ANSWER!
Now we must substitute X into the exterior angles equation!
So: 3(50) -8
150-8
142
So your exterior angle (PRS) would be B.) 142 degrees

Answer 2

b

Explanation:

∠ QRP and ∠ PRS are a linear pair and sum to 180° , that is

∠ QRP + 3x - 8 = 180 ( subtract 3x - 8 from both sides )

∠ QRP = 180 - (3x - 8) = 180 - 3x + 8 = 188 - 3x

the sum of the 3 angles in Δ PQR = 180° , that is

188 - 3x + x + 2 + 90 = 180

- 2x + 280 = 180 ( subtract 280 from both sides )

- 2x = - 100 ( divide both sides by - 2 )

x = 50

Then

∠ PRS = 3x - 8 = 3(50) - 8 = 150 - 8 = 142°