Question

Rays QR and QS are perpendicular. Point T lies in the interior of ∠RQS . If m∠RQT=(7w+12)° and m∠SQT=(9w−18)° , find m∠RQT and m∠SQT . m∠RQT = ° m∠SQT = °

Answer 1

To find the measures of angles RQT and SQT, set up an equation using the sum of angles in a triangle. Simplify the equation and solve for w. Substitute the value of w back into the expressions for the angles to find their measures.

Step-by-step explanation:

To find the measures of angles RQT and SQT, we can set up an equation using the fact that the sum of the measures of angles in a triangle is 180 degrees.

Given that m∠RQT = (7w+12)° and m∠SQT = (9w-18)°, we can set up the equation as:

(7w+12) + (9w-18) + 90 = 180

Simplifying the equation, we have:

16w + 84 = 180

Subtracting 84 from both sides:

16w = 96

Dividing both sides by 16:

w = 6

Now we can substitute the value of w back into the expressions for the angles:

m∠RQT = (7(6)+12)° = 54°

m∠SQT = (9(6)-18)° = 36°