Question

Two opposite angle of parallelogram are(5x - 21) and (x + 75) find the the measure of each the angle of the parallelogram

Answer 1

Answer:

The angles of the Parallelogram are -

• 99°
• 81°
• 99°
• 81°

Step-by-step explanation:

Given :

Opposite angles of a triangle = (5x - 21) and (x + 75)

To find :

The measure of the angles

Solution :

We know that -

Opposite angles in a parallelogram are equal.

$\longrightarrow$ (5x - 21) = (x + 75)

$\longrightarrow$ 5x - x = 75 + 21

$\longrightarrow$ 4x = 96

$\longrightarrow$ x = 96/4

$\longrightarrow$ x = 24

$\rule{300}{1.5}$

★ Value of (5x - 21)

$\longrightarrow$ 5(24) - 21

$\longrightarrow$ 120 - 21

$\longrightarrow$ 99

One angles is = 99°

The second angle will also be 99°

$\rule{300}{1.5}$

Consider the other 2 opposite angles as y (as they are same)

According to the Angle Sum property of parallelogram, All angles in a parallelogram sum up and make 360°.

$\longrightarrow$ 99 + 99 + y + y = 360

$\longrightarrow$ 198 + 2y = 360

$\longrightarrow$ 2y = 360 - 198

$\longrightarrow$ 2y = 162

$\longrightarrow$ y = 162/2

$\longrightarrow$ y = 81°

$\therefore$ The angles of the Parallelogram are -

• 99°
• 81°
• 99°
• 81°