Question

1. point s is in the interior of ∠pqr. if m∠pqs = 4x and m∠sqr = 6x + 5, and m∠pqr = 105, find the value of x.

a) x = 10
b) x = 10.5
c) x = 12
d) x = 9.5
○ a) x = 10
○ b) x = 10.5
○ c) x = 12
○ d) x = 9.5

Explanation:

Step1: Set up equation

Since point S is in the interior of $\angle PQR$, we know that $m\angle PQS + m\angle SQR=m\angle PQR$. So, $4x+(6x + 5)=105$.

Step2: Simplify left - hand side

Combine like terms: $(4x+6x)+5 = 10x + 5$. The equation becomes $10x+5 = 105$.

Step3: Isolate the variable term

Subtract 5 from both sides: $10x+5 - 5=105 - 5$, which gives $10x=100$.

Step4: Solve for x

Divide both sides by 10: $\frac{10x}{10}=\frac{100}{10}$, so $x = 10$.

Answer:

A. $x = 10$