Question

If figure , ABCD
is a parallelogram
with angel B= 100° and angel DAC = so then
find value of x.​

Answer 1

we know that opposite angles of parallelogram is equal

Angle B=100°

therefore , Angle D=100°[opposite angles of a parallelogram]

Angle c or y =180°-100°=80°[adjacent angle of Angle D]

and we know that sum of adjacent Angle is 180°

opposite angle of c =Angle A

Angle A =80°[opposite angle of Angle c]

Angle A =50°+x

therefore,x=80°-50°=30°

parallelogram

A parallelogram is a special type of quadrilateral that has equal and parallel opposite sides. The given figure shows a parallelogram ABCD which as AB parallel to CD and AD parallel to BC. Also, AD = BC and AB = CD. We also see a lot of parallelogram like shapes and objects around us.

Area: base × height

Perimeter: 2 x (sum of lengths of adjacent sides)

Number of vertices: 4

Number of edges: 4

Properties: Convex polygon

Type: Quadrilateral

Line of symmetry: 0

Answer 2

Given :-

• ABCD is a parallelogram
• ∠B = 100°
• ∠DAC = 50°

To Find :-

• value of x ?

Solution :-

DA || BC

then,

∠DAC = ∠BCA (alternative angles)

➪ ∠BCA = 50°

now, in triangle ABC

∠BAC + ∠B + ∠BCA = 180°

(angle sum property of triangle)

$\bold{: \implies x +100 \degree + 50 \degree= 180 \degree } \\ \\ \bold{: \implies x + 150 \degree = 180 \degree } \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies x = 180 \degree - 150 \degree} \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies \boxed { \bold{ x = 30 \degree }}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

now,

∠BAC = ∠DCA (alternate angles)

➪ ∠DCA = 30°

and

∠C = ∠DCA + BCA

➪ ∠C = 30° + 50°

➪ y = 80°

hence, value of x is 30° and value of y is 80°