Question

In the figure, `square`ABCD is a cyclic quadrilateral. Seg AB is a diameter. If ∠ ADC = 120˚, complete the following activity to find measure of ∠ BAC.

`square` ABCD is a cyclic quadrilateral.
∴ ∠ ADC + ∠ ABC = 180°
∴ 120˚ + ∠ ABC = 180°
∴ ∠ ABC = ______
But ∠ ACB = ______  .......(angle in semicircle)

In Δ ABC,
∠ BAC + ∠ ACB + ∠ ABC = 180°
∴ ∠BAC + ______ = 180°
∴ ∠ BAC = ______

Answer 1

`square` ABCD is a cyclic quadrilateral.
∴ ∠ ADC + ∠ ABC = 180°
∴ 120 + ∠ ABC = 180°
∴ ∠ABC = 60°
But ∠ ACB = 90° ................... (Angle in semicircle)
In Δ ABC,
∠ BAC + ∠ ACB + ∠ ABC = 180°

∴ ∠ BAC + 90°+ 60° = 180°
∴ ∠ BAC + 150° = 180°
∴ ∠ BAC = 180°- 150°
∴ ∠ BAC = 30°