Question

$\angle pqr$ is a right angle. find $m\angle pqs$ and $m\angle sqr$. enter deg after any value that is in degrees.

a) $m\angle pqs$
$m\angle pqs = $

b) $m\angle sqr$
$m\angle sqr = $

Explanation:

Step1: Set up the equation

Since $\angle PQR$ is a right angle, its measure is $90^\circ$. The sum of $\angle PQS$ and $\angle SQR$ is equal to $\angle PQR$. So we have the equation:
$$(9x - 75) + 2x = 90$$

Step2: Solve for x

Combine like terms:
$$11x - 75 = 90$$
Add 75 to both sides:
$$11x = 90 + 75$$
$$11x = 165$$
Divide both sides by 11:
$$x = \frac{165}{11}$$
$$x = 15$$

Step3: Find $m\angle PQS$

Substitute $x = 15$ into the expression for $\angle PQS$:
$$m\angle PQS = (9x - 75)^\circ = (9\times15 - 75)^\circ = (135 - 75)^\circ = 60^\circ$$

Step4: Find $m\angle SQR$

Substitute $x = 15$ into the expression for $\angle SQR$:
$$m\angle SQR = (2x)^\circ = (2\times15)^\circ = 30^\circ$$

Answer:

a) $m\angle PQS = 60$ deg
b) $m\angle SQR = 30$ deg