Question

2. Find the value of x and y in given figures :
​

Answer 1

1. ∵ AB = AC

∴ ∠ACB = ∠ABC = x [∠s opp. to eq. sides of ∆are eq.]

Now in ∆ABC,

∠A + ∠B + ∠C = 180° [∠ sum prop.]

⇒90° + x+x = 180°

⇒2x = 90°

⇒x = 45°

Now, x + 90° = y. [ext. ∠ prop.]

⇒y = 45°+90° = 135°

2. ∵ BA = BC

∴ ∠BCA = ∠BAC = x [∠s opp. to eq. sides of ∆are eq.]

Now, ∠BCA = 20°. [V.O.A.]

⇒x = 20°

Now, in ∆ABC,

∠A + ∠B + ∠C = 180° [∠ sum prop.]

⇒x+y+x = 180°

⇒20°+y+20° = 180°

⇒y = 180°-40° = 140°