Question

if ∠rqt = 155, what are m∠rqs and m∠tqs? (4x - 20)° (3x + 14)°

Explanation:

Step1: Set up equation based on angle - sum

Since $\angle RQT=\angle RQS+\angle TQS$, we have $(4x - 20)+(3x + 14)=155$.
Combining like - terms: $4x+3x-20 + 14=155$, which simplifies to $7x-6 = 155$.

Step2: Solve for x

Add 6 to both sides of the equation: $7x-6 + 6=155 + 6$, so $7x=161$.
Divide both sides by 7: $x=\frac{161}{7}=23$.

Step3: Find $\angle RQS$

Substitute $x = 23$ into the expression for $\angle RQS$: $\angle RQS=4x-20=4\times23-20=92 - 20=72^{\circ}$.

Step4: Find $\angle TQS$

Substitute $x = 23$ into the expression for $\angle TQS$: $\angle TQS=3x + 14=3\times23+14=69 + 14=83^{\circ}$.

Answer:

$m\angle RQS = 72^{\circ}$, $m\angle TQS = 83^{\circ}$