Question

question 1 of 17
angle pqr is a right angle.
the measure of angle pos is 35°.
the measure of angle sqr is x°.
what is the value of x?
question 2 of 17
given the figure below, find the values of x and z.
question 3 of 17
in the figure below, m∠1=(x + 12)° and m∠2=5x°.
find the angle measures.
question 4 of 17
(a) an angle measures 59°. what is the measure of its complement?
(b) an angle measures 137°. what is the measure of its supplement?
question 5 of 17
in the figure, m∠1=(3x)° and m∠2=(x + 88)°.
(a) write an equation to find x. make sure you use the
sign in your answer.
equation:
(b) find the degree measure of each angle.
m∠1=
°
m∠2=
°

Explanation:

Step1: Analyze the relationship between angles

Since \(\angle PQR\) is a right - angle (\(90^{\circ}\)), and \(\angle PQR=\angle PQS+\angle SQR\). Given \(\angle PQS = 35^{\circ}\) and \(\angle SQR=x^{\circ}\).

Step2: Set up the equation

Using the angle - addition formula for \(\angle PQR\), we have \(x + 35=90\).

Step3: Solve for \(x\)

Subtract 35 from both sides of the equation: \(x=90 - 35\).

Answer:

\(x = 55\)