Question

Find ${\left(x+y\right)}^2$, where ∠SQR = 20° and ∠QSP = 30°. [1 mark]

• A. 18000
• B. 130
• C. 16900
• D. 2500

Answer 1

The correct option is C 16900

∠PQR & ∠PSR are subtended by chord PR Hence;

∠PQR + ∠PSR = 180°

(x° + 20°) + (y° + 30°) = 180°

x° + y° = 180° - 20° - 30°

x° + y° = 130°

Let’s square both the sides,${\left(x+y\right)}^2={\left(130\right)}^2$

Therefore, ${\left(x+y\right)}^2=16900$