Answer:
The m∠ V is 58°.
Step-by-step 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°
