Question

(2x - 30) and (x + 60) are a pair of complementary angles.
Find the following values:
The smaller angle is :
The greater angle is :​

Answer 1

Step-by-step explanation:

the smaller angle is 10 and greater angle is 80

Answer 2

Answer :-

• The two angles are 10° and 80°.
• 10° is the smaller angle and 80° is the greater angle.

Given :-

• (2x - 30)° and (x + 60)° are a pair of complementary angles.

To find :-

• The smaller and the greater angle.

Step-by-step explanation :-

Two complementary angles are (2x - 30)° and (x + 60)°.

We know that complementary angles add up to 90°.

So, if we add these two angles, they must be equal to 90°.

Therefore, we get :-

$\sf (2x - 30)^{\circ} + (x + 60)^{\circ} = 90^{\circ}$

Removing the brackets,

$\sf 2x^{\circ} - 30^{\circ} + x^{\circ} + 60^{\circ} = 90^{\circ}$

Putting the constants and variables separately,

(- 30 + 60 = 30)

$\sf 2x^{\circ} + x^{\circ} - 30^{\circ} + 60^{\circ} = 90^{\circ}$

On simplifying,

$\sf 3x^{\circ} + 30^{\circ} = 90^{\circ}$

Transposing 30 from LHS to RHS, changing its sign,

$\sf 3x^{\circ} = 90^{\circ} - 30^{\circ}$

Subtracting,

$\sf 3x^{\circ} = 60^{\circ}$

Transposing 3 from LHS to RHS, changing its sign,

$\sf x^{\circ} = \dfrac{60^{\circ}}{3}$

Dividing 60 by 3,

$\sf x^{\circ} = 20^{\circ}$

The value of x is 20°.

So, the value of the angles are as follows :-

(2x - 30)° = 2° × 20° - 30° = 40° - 30° = 10°.

(x + 60)° = 20° + 60° = 80°.

Thus, the smaller angle is 10° and the greater angle is 80°.

Verification :-

To check our answer, lets add these two angles and see whether they add up to 90°.

80° + 10° = 90°.

Since they add up to 90°,

Hence verified! ✔️✔️