Question
In this figure, angle R and angle Q are complementary.
What is the measurement of angle R?
Triangle PQR is a right angle. Angle P is 90 degrees, angle Q is 53 degrees, and angle R is labeled x degrees.
Angle R is
degrees.
What is the measurement of angle R?
Triangle PQR is a right angle. Angle P is 90 degrees, angle Q is 53 degrees, and angle R is labeled x degrees.
Angle R is
degrees.
Answers
GPT-4o mini
In triangle PQR, since it is a right triangle, the sum of the angles is 180 degrees. Given that Angle P is 90 degrees and Angle Q is 53 degrees, we can find the measurement of Angle R.
According to the triangle angle sum property:
\[
\text{Angle P} + \text{Angle Q} + \text{Angle R} = 180^\circ
\]
Substituting the known values:
\[
90^\circ + 53^\circ + x = 180^\circ
\]
Now, combine the angles:
\[
143^\circ + x = 180^\circ
\]
To isolate \(x\), subtract 143 degrees from both sides:
\[
x = 180^\circ - 143^\circ
\]
Calculating that gives:
\[
x = 37^\circ
\]
Therefore, the measurement of angle R is **37 degrees**.
According to the triangle angle sum property:
\[
\text{Angle P} + \text{Angle Q} + \text{Angle R} = 180^\circ
\]
Substituting the known values:
\[
90^\circ + 53^\circ + x = 180^\circ
\]
Now, combine the angles:
\[
143^\circ + x = 180^\circ
\]
To isolate \(x\), subtract 143 degrees from both sides:
\[
x = 180^\circ - 143^\circ
\]
Calculating that gives:
\[
x = 37^\circ
\]
Therefore, the measurement of angle R is **37 degrees**.