Question

XYZ is angled isosceles in which angle XYZ. = 90 degree. YZ has been produced to A. Verify that angle XZA = 3 XZY

Answer 1

1. Step-by-step explanation:

hope it will help you

Answer 2

∠ XZA = 3 × ∠ XZY {Verified}

Step-by-step explanation:

See the attached diagram.

Given that Δ XYZ is an isosceles triangle with XY = YZ and ∠ YXZ = ∠ YZX = p Degrees (Say)

Now, given that ∠ XYZ = 90°.

So, from Δ XYZ,

∠ XYZ + ∠ YZX + ∠ YXZ = 180°

⇒ 90° + p° + p° = 180°

⇒ 2p° = 90°

⇒ p° = 45°.

Now, YZ is produced to A.

Then, ∠ XZY + ∠ XZA = 180° {Since, they are supplementary}

⇒ 45° + ∠ XZA = 180°

⇒ ∠ XZA = 180° - 45° = 135° = 3 × 45° = 3p°

So, ∠ XZY = p° and ∠ XZA = 3p°

Hence, ∠ XZA = 3 × ∠ XZY {Verified}