Question

Observe the figures below and write the measure of the remaining angle of the quadrilaterals.

Answer 1

(1) We know that the sum of the angles of a quadrilateral is 360°
∴ In $\square$ WXYZ,
m $\angle$W + m $\angle$X + m $\angle$Y + m $\angle$Z = 360°
⇒130° + 100° + m$\angle$Y + 40° = 360°
⇒ m $\angle$Y + (100° + 40° + 130°) = 360°
⇒ m $\angle$Y + 270° = 360°
⇒ m $\angle$Y = 360° - 270°
⇒ m$\angle$Y = 90°

(2) We know that the sum of the angles of a quadrilateral is 360°
∴ In $\square$KLMN,
m $\angle$K + m $\angle$L + m $\angle$M + m $\angle$N = 360°
⇒ 90° + 90° + 90° + m $\angle$N = 360°
⇒ (90° + 90° + 90°) + m $\angle$N = 360°
⇒ 270° + m $\angle$N = 360°
⇒ m $\angle$N = 360° - 270°
⇒ m $\angle$N = 90°