Question

∠rqs and ∠tqs are a linear pair where m∠rqs = (5x + 5)° and m∠tqs = (2x + 21)°.
a. solve for x.
b. find m∠rqs and m∠tqs.
c. show how you can check your answer.

1. solve for x.
2. = \boxed{}

Explanation:

Step1: Set up linear pair equation

Linear pair sums to $180^\circ$:
$$(5x+5)+(2x+21)=180$$

Step2: Simplify the equation

Combine like terms:
$$7x+26=180$$

Step3: Solve for x

Isolate x:
$$7x=180-26=154$$
$$x=\frac{154}{7}=22$$

Step4: Calculate angle measures

Substitute $x=22$:
$$m\angle RQS=5(22)+5=115^\circ$$
$$m\angle TQS=2(22)+21=65^\circ$$

Step5: Check the solution

Sum the two angles:
$$115+65=180^\circ$$
This matches the linear pair requirement.

Answer:

a. $x=22$
b. $m\angle RQS=115^\circ$, $m\angle TQS=65^\circ$
c. Verified, the answer is correct