Question

The adjacent figure HOPE is a parallelogram. Find the angle measure x, y and z. State the properties you use to find them.

Answer 1

Let ∠HOP be a.

70° + a = 180°

| ∵ Sum of an Exterior angle and an interior angle in any polygon is 180°.

a = 180° - 70°

a = 110°.

So,

➜ x = 110°.

| ∵ Opposite angles of a llgm are equal.

And (40+z)° + 110°= 180°

| ∵ Sum of two Adjacent Angles is 180°

z + 150° = 180°

z = 180° - 150°

➜ z = 30°.

And z + y + a = 180°

| ∵ Angle Sum property.

30° + y + 110° = 180°

y + 140° = 180°

y = 180° - 140°

➜ y = 40°

Answer 2

$\huge\mathrm{Properties :-}$

• In parallelogram opposite angles are equal
• In parallelogram opposite sides are parallel

Answers ➡

x = 110°

y = 40°

z = 30°

➡ Refer to the above attachment