Question

I have been trying to solve problem 5 and 6 for 30 mins​

Answer 1

Answer:

#5

x = 45

E

Step-by-step explanation:

Theorems you need:

• The measures of 2 adjacent angles that form a straight line with the outer sides add up to 180°.
• The sum of the interior angles of a triangle add up to 180° ((n-2)×180).

#5

Knowing those, you first want to find the triangle's 3 interior angles.

The angles <QSO & <QSR are adjacent (share a common ray) and form a straight line with the outer rays, therefore they add up to 180.

So m<QSO+m<QSR=180.

Rewrite the equation: m<QSR=180-m<QSO

Plug the known value in: m<QSR=180-(3x-17)

Distribution & Combining like terms: m<QSR=180-3x+17=197-3x

Now solve for the 3 interior angles to equal 180.

(197-3x)+(25)+(2x+3)=180

Combine like terms: 225-x=180

Isolate the x term (-225 to both sides): -x=180-225=-45

Isolate the x (×-1 to both sides):

x=45