Question

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Answer 1

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Answer 2

Angle Q = 56°

Angle S = 104°

Angles QPS and Angle Angle QRS are in the ratio 2:3

Let Angles QPS and Angle Angle QRS be 2x and 3x respectively.

We know that the sum of all the angles of any quadrilateral is 360° (property of any quadrilateral).

Thus, ATQ

56 + 104 + 2x + 3x = 360

= 160 + 5x = 360

= 5x = 360 - 160 (transpositioning)

= 5x = 200

= x = $\large {\frac{200}{5} }$

= x = 40

Therefore: Angles QPS = 2x

= 2 × 40

= 80°

Angles QRS = 3x

= 3 × 40

= 120°

Now, Qp and Rs are straight lines.

Hence,

Angle a = 180 - Angles QPS (Adjacent Angles)

= 180 - 80

= 100° (Ans)

Angle b = 180 - Angles QRS (Adjacent Angles)

= 180 - 120

= 60° (Ans)

Hope this helped...