Question

in the diagram, $m\angle qrs = 133^circ$.

diagram of triangle pqr with angle at p: $(3x + 4)^circ$, angle at q: $(5x + 9)^circ$, and rs is a ray extending from r, making a straight line with pr. then the question: what is the value of $x$? enter the answer in the space provided. use numbers instead of words. $x = \square$

Explanation:

Step1: Recall the exterior angle theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(m\angle QRS=(3x + 4)+(5x+9)\).

Step2: Substitute the given value and solve for x

We know that \(m\angle QRS = 133^{\circ}\), so we set up the equation:
\(3x + 4+5x + 9=133\)
Combine like terms: \(8x+13 = 133\)
Subtract 13 from both sides: \(8x=133 - 13=120\)
Divide both sides by 8: \(x=\frac{120}{8} = 15\)

Answer:

15