In parallelogram PQRS, P is three times Q. What is S?

Question 45

EasyOriginal question

In parallelogram PQRS, $\angle P$ is three times $\angle Q$ . What is $\angle S$ ?

45°Correct answerYour answer60°Correct answerYour answer135°Correct answerYour answer270°Correct answerYour answer

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CorrectNot quiteAnswer A

Correct answer: A

Adjacent angles of a parallelogram add up to 180°: $\angle P + \angle Q = 180^\circ$ .
$3\angle Q + \angle Q = 180^\circ$ , so $\angle Q = 45^\circ$ and $\angle P = 135^\circ$ .
$\angle S$ is opposite $\angle Q$ , so $\angle S = 45^\circ$ .

Worth noting

$\angle S$ is opposite $\angle Q$ , not $\angle P$ , so it is the smaller angle. 60° comes from dividing 180° by 3 instead of by 4.

Concept: Adjacent angles of a parallelogram are supplementary; opposite angles are equal
Typical timeTypical: 40 s
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