PYQ Vault
EbooksTutor

Point on a side where the exterior angle is twice a part of the vertex angle: find the other angle at that point

The same question, asked 2 times: 29 Jan 2022 Tier II*, 3 Feb 2022 Tier II. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    29 Jan 2022 Tier II

    16
    In △PQR\triangle PQR, SS is a point on the side QRQR such that ∠QPS=12∠PSR\angle QPS = \frac{1}{2}\angle PSR, ∠QPR=78∘\angle QPR = 78^\circ and ∠PRS=44∘\angle PRS = 44^\circ. What is the measure of ∠PSQ\angle PSQ?

    Tap an option to check your answer.

  2. Question 2

    3 Feb 2022 Tier II

    81
    In △ABC\triangle ABC, D is a point on BC such that ∠ADB=2∠DAC\angle ADB = 2\angle DAC, ∠BAC=70∘\angle BAC = 70^\circ and ∠B=56∘\angle B = 56^\circ. What is the measure of ∠ADC\angle ADC?

    Tap an option to check your answer.