Question

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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°

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Answer 1

Answer: The correct options for blank 1,2 and 3 are B, F and C respectively.

Explanation:

It is given that the ∠PQR and ∠RQS are supplementary angles and ∠PQR=115°.

The two angles are called supplementary angles if they are  lies on the same arc of a straight line and their sum is 180 degree.

Since it is given that ∠PQR and ∠RQS are supplementary angles, so by the definition of supplementary angles we can say that their sum is 180 degree.

$\angle PQR+\angle RQS=180^{\circ}$    .... (1)

Therefore, the correct option for first blank is option B.

It is given that ∠PQR=115°.

Using the substitution property of equality, the equation (1) can be written as,

$115^{\circ}+\angle RQS=180^{\circ}$

Therefore, the correct option for second blank is option F.

Using the subtraction property of equality, ​​ ∠PQR=65° .

An angle less that 90 degree is called an acute angle and the an angle more than 90 degree but not more that 180 degree is called an obtuse angle.

Since 65 is less than 90, so by the definition of acute angle the ∠RQS ​ is an acute angle.

Therefore, the correct option for third blank is option C.

Answer 2

Definition of acute angle