Question

ABCD is a parallelogram. Angle B = 5x + 25 degree and Angle D = 8x - 5 degree. Find x and angle C . Please help​

Answer 1

Answer:

x=10 , angle C = 105

Step-by-step explanation:

8x-5=5x+25 (diagonals of a parallelogram are equal)

8x-5x=30

x=30÷3,. x=10

angle C =

360=2×75+2x

360- 150=2x

2x= 210

x=105

Answer 2

Answer:

• x = 85°
• ∠C = 105°

Explanation:

In the ||gm ABCD,

∠B = (5x + 25)° and ∠D = (8x - 5)°

Find the value of ‘x’ and ∠C

Recall, the property of a ||gm.

Opposite angles are equal.

$\rm \therefore \angle B = \angle D$

Solving for ‘x’ :-

$\rm \implies \: (5x + 25)^{ \circ} = (8x - 5)^{ \circ}$

$\rm \implies \: 5x + 25 = 8x - 5$

$\rm \implies \: 25 + 5 = 8x - 5x$

$\rm \implies \: 30 = 3x$

$\rm \therefore \: x = {10}^{ \circ}$

Therefore, the value of ‘x’ is 10°

Now

Recalling the property again,

• Adjacent angles of a ||gm is equal to 180°

$\rm \therefore \: \angle D + \angle C = {180}^{ \circ}$

Where,

• ∠D = 8x - 5 = 8(10) - 5 = 75°

Substituting ∠D :-

$\rm \implies \: 75^{ \circ} + \angle C = {180}^{ \circ}$

$\rm \implies \: \angle C = {180}^{ \circ} - 75^{ \circ}$

$\rm \implies \: \angle C = {105}^{ \circ}$

Hence, ∠C is 105°

______________________________

Properties of a parallelogram:

• Opposite angles are equal.
• Diagonals are equal.
• Adjacent angels sums to 180°