# Mathematics Questions and Answers – Pair of Angles

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Pair of Angles”.

1. If a ray stands on a line, then the sum of two adjacent angle is 180°.
a) True
b) False

Explanation: As shown in below diagram, we can see that ray OQ stands on line PQ. We know that angle formed by a line is 180° so angle formed by the line PQ is 180°.
We also know that for two adjacent angles ∠POR and ∠ROQ,
∠POR + ∠ROQ = ∠POQ = angle formed by line PQ = 180°.

2. From the given diagram, if ∠SOQ : ∠ROQ = 2 : 3, then what are the values of angles ∠SOQ and ∠ROQ? a) 54° and 36°
b) 40° and 60°
c) 72° and 48°
d) 72° and 108°

Explanation: We know from axiom 6.1 that if a ray stands on a line, then the sum of two adjacent angle is 180°.
Here, ∠SOQ and ∠ROQ are two adjacent angles.
Hence, ∠SOQ + ∠ROQ = 180° and ∠SOQ : ∠ROQ = 2 : 3
Therefore, ∠SOQ = 2/(2+3) * 180
= 2/5 * 180
= 72°
And
∠ROQ = 3/(2+3) * 180
= 3/5 * 180
= 108°.

Sanfoundry Global Education & Learning Series – Mathematics – Class 9. 