It is given that ∠PQR and ∠RQS are supplementary angles. So, m∠PQR+m∠RQS=180° using the B. definition of supplementary angles. It is also given that m∠PQR=115°. Using the substitution property of equality, F. 115° + m∠RQS=180° . Using the subtraction property of equality, m∠PQR=65°. Therefore, ∠RQS is an acute angle by C. definition of acute angle.
In Mathematics and Geometry, supplementary angles refers to two (2) angles or arc whose sum is equal to 180 degrees.
Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. Since angles PQR and RQS form exterior sides of opposite rays, we have the following angle sum based on the definition of supplementary angles;
m∠PQR + m∠RQS = 180°
By using the substitution method, we can logically deduce the following supplementary angles based on linear pairs theorem:
115° + m∠RQS = 180°
m∠RQS = 180° - 115°
m∠RQS = 65°
In conclusion, ∠RQS is an acute angle by the definition of acute angle because it is less than 90 degrees.
Complete Question:
Given: ∠PQR and ∠RQS are supplementary angles and m∠PQR=115°
Prove: ∠RQS is an acute angle.
It is given that ∠PQR and ∠RQS are supplementary angles. So, m∠PQR+m∠RQS=180° using the ________ . It is also given that m∠PQR=115° . Using the substitution property of equality, ________ + m∠RQS=180° . Using the subtraction property of equality, m∠PQR=65° . Therefore, ∠RQS is an acute angle by ________ .
A. definition of complementary angles
B. definition of supplementary angles
C. definition of acute angle
D. definition of obtuse angle
E. 180°
F. 115°