Question

c).In the following parallelograms find the measures of the angle marked

as x,y z​

Answer 1

Answer:

In a parallelogram opposite sides and angles are equal

⇒4x-3 = 3x+2

  x = 5

AB and DC are two parallel lines and AC is a transversal

⇒ y+10 = 35 (alternate interior angles)

    y = 35-10 = 25°

⇒y+10+70+z = 180°(Angle sum theorem of a triangle)

   25°+10°+70°+z  = 180°

  z = 180 - 105 = 75°

Answer 2

Step-by-step explanation:

For x :-

We know that parallel sides are equal

so,

⟹ 4x - 3 = 3x + 2

⟹ 4x - 3x = 3 + 2

⟹ x = 5 ans.

For z :-

We can say that angle CAB = angle ACD

[∵ opposite angles are equal]

So,

⟹ y + 10° = 35°

⟹ y = 35° - 10°

⟹ y = 25°

In ∆ ABC, For z

To find y we know that sum of all angles of a triangle is 180° hence, we can write it as,

⟹ (y + 10°) + 70° + z = 180°

⟹ 35° + 70° + z = 180°

⟹ z + 105° = 180°

⟹ z = 180° - 105°

⟹ z = 75° ans