Find the measure of an angle, if seven times its complement is 10 less than three times its supplement - Maths - Lines and Angles

Question

Find the measure of an angle, if seven times its complement is
10 less
than three times its supplement

Vimala · Accepted Answer

Let the angle to be determined be $∠ A$ .

Sum of an angle and its complement is $90^{\circ}$

Sum of an angle and its supplement is $180^{\circ}$

Thus,

Complement of the angle is $90^{\circ} - ∠ A$

Supplement of the angle is $180^{\circ} - ∠ A$

It is given that:

$7 (90^{\circ} - ∠ A) = 3 (180^{\circ} - ∠ A) - 10 630^{\circ} - 7 ∠ A = 540^{\circ} - 3 ∠ A - 10 630^{\circ} - 7 ∠ A = 530^{\circ} - 3 ∠ A 4 ∠ A = 100^{\circ} ∠ A = 25^{\circ}$

Thus, the measure of the angle is $25^{\circ}$

Find the measure of an angle, if seven times its complement is 10 less than three times its supplement.

Find the measure of an angle, if seven times its complement is 10 less

than three times its supplement.