Question

If one angle ofa parallelogramis 30° less then other angle,then what is the larger area?

Answer 1

Question : -

If one angle of a parallelogram is 30° less than the other angle, then which is the largest angle among them?

Answer : -

Construction : -

Draw a ||logram say ABCD. Extend A to E, B to F, A to H and B to G as shown in the above attachment.

As we know,

The opposite angles of a ||logram are equal and angle sum property of a ||logram is 360°.

Also, the angles lying on the same side of the transversal are supplementary meaning that sum of both the angles is 180°.

As one angle is 30° less than the other one.

So, let x be the unknown number.

Therefore, our angles will be,

x and x - 30°

Let ∠CBA = x and ∠DAB = x - 30°

From the above figure,

∠CBA + ∠DAB = 180°

[Supplementary angles meansures 180°].

[By substituting the above values,]

x + x - 30° = 180°

2x - 30° = 180°

2x = 180° + 30

2x = 210

x = $\frac{210}{2}$

x = $\frac{\cancel{210}}{\cancel{2}}$

x = 105

So, we've gotta the value of x. Now we'll substitute 105 in the place of x.

[By substituting the value of x],

∠CBA = x = 105°

∠DAB = x - 30°

=> ∠DAB = 105 - 30°

=> ∠DAB = 75°

=> So, the angles are 75° and 105°.

Verification : -

Substitute 75° and 105° in the place of x.

From the above figure,

∠CBA + ∠DAB = 180°

[Supplementary angles measures 180°].

x + x - 30° = 180°

[But, x = 105° and x - 30° = 75°]

.°. 105° + 75° = 180°

=> 180° = 180°

Hence, verified.

.°. Angles are 75° and 105°.

Therefore, ∠CBA is the largest angle among them.