Question

Find the value of x
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Answer 1

Required Solution:

Construct angle 1 and angle 2 as shown in picture

Now Let's find there values:

To find angle 1:

• ∠1 + 70°=180°

Reason:

Linear Pair

• ∠1 = 180° - 70°

• ∠1 = 110°

To find angle 2:

• ∠2 + 60° = 180°

• ∠2 = 180° - 60°

• ∠2 = 120°

As we can see the given figure is a pentagon, therefore sum of angles of the figure is equal to 540°.

So:-

• x + x + ∠1 + ∠2 + 30° = 540°

• x + x + 110° + 120° +30°= 540°

• x + x + 230° + 30°= 540°

• 2x + 260° = 540°

• 2x = 540° - 260°

• 2x =280 °

• x = 280°/2

• x = 140°

Now Let's Verify the value of x

• x + x + ∠1 + ∠2 + 30°= 540°

put value of x in this equation

• 140° + 140° + ∠1 + ∠2 + 30°= 540

• 140° + 140° + 110° + 120° + 30° = 540°

• 280° + 230° + 30° = 540°

• 0° = 540° -280° - 230° - 30°

• 0° = 540 -280° -260°

• 0° = 540° - 540°

• 0° = 0°

LHS = RHS

Hence verified!

.°. Value of x = 140°