Question

Need help on a geometry question

Answer 1

The m∠ V is 58°.

Explanation:

Given:

∠ U = 18°

∠ W = 52°

∠ X = 24°

To Find:

∠ V = ?

Solution:

In Δ WYX

∠ YWX + ∠ WXY + ∠ WYX = 180°.....{sum of the angles of a triangle is 180°}

∴ 52 + 24 + ∠ WYX = 180°

∴ ∠ WYX = 180 - 76

∴ ∠ WYX = 104°

Now,

∠ VYU = ∠ WYX = 104° .........{vertically opposite angles are equal}

Now in Δ VYU

∠ VYU + ∠ VUY +∠ UVY = 180° {sum of the angles of a triangle is 180°}

∴ 104 + 18 + ∠ UVY = 180°

∴ ∠ UVY = 180 - 122

∴ ∠ UVY = 58

∴ ∠ V = 58°