Question

consider the following parallelogram find value of x y z​

Answer 1

( i ) Find x, y and z

Answer: z = 100°, x = 50° and y = 50°

Explanation:

⟹ z = 100° ( Opposite angles of a parallelogram)

⟹ z + ∠ABD = 180° ( Adjacent angles of ||gram )

⟹ z + 30° + x = 180° ( ∠ABD = 30° + x )

⟹ 100° + 30° + x = 180°

⟹ 130° + x = 180°

⟹ x = 180° - 130°

⟹ x = 50°

⟹ x = y ( Alternate interior angles )

⟹ 50° = y

(ii) Find x, y and z

Answers : x = 90°, z = 65° and y = 65°

Explanation:

x = 90° ( vertically opposite angles )

x + z + 25° = 180° (Angle sum property of triangle)

⟹ 90° + z + 25° = 180°

⟹ 115° + z = 180°

⟹ z = 180° - 115°

⟹ z = 65°

y = z ( alternate interior angles )

⟹ y = 65°

(iii) Find x

Answer: x = 115°

Explanation:

Sum of all angles of a quadrilateral is 360°

⟹ 90° + 90° + 65° + x = 360°

⟹ 245° + x = 360°

⟹ x = 360° - 245°

⟹ x = 115°

(iv) Find x

Answer: x = 40°

Explanation:

ABCD and PQRS are ||grams

∠A + ∠ABC = 180° ( Adjacent angles )

⟹ 110° + ∠ABC = 180°

⟹ ∠ABC = 180° - 110°

⟹ ∠ABC = 70°

∠SPQ = ∠R ( Opposite angles of ||gram )

⟹ ∠SPQ = 70°

∠SPQ + ∠ABC + x = 180° ( Angles of a triangle )

⟹ 70° + 70° + x = 180°

⟹ 140° + x = 180°

⟹ x = 180° - 140°

⟹ x = 40°