Find the measure of an angle which is(i) Equal to its complement(ii) E

1.	Find the measure of an angle which is(i) Equal to its complement(ii) Equal to its supplement
Answer» (i) Consider the required angle as x° We know that the complement can be written as 90° – x° To find that the measure of an angle is equal to its complement We get x° = 90° – x° We can also write it as x + x = 90 So we get 2x = 90 By division we get x = 90/2 x° = 45° Therefore, the measure of an angle which is equal to its complement is 45° (ii) Consider the required angle as x° We know that the supplement can be written as 180° – x° To find that the measure of an angle is equal to its complement We get x° = 180° – x° We can also write it as x + x = 180 So we get 2x = 180 By division we get x = 180/2 x° = 90° Therefore, the measure of an angle which is equal to its complement is 90°

Find the measure of an angle which is(i) Equal to its complement(ii) Equal to its supplement

Answer»

(i) Consider the required angle as x°

We know that the complement can be written as 90° – x°

To find that the measure of an angle is equal to its complement

We get

x° = 90° – x°

We can also write it as

x + x = 90

So we get

2x = 90

By division we get

x = 90/2

x° = 45°

Therefore, the measure of an angle which is equal to its complement is 45°

(ii) Consider the required angle as x°

We know that the supplement can be written as 180° – x°

To find that the measure of an angle is equal to its complement

We get

x° = 180° – x°

We can also write it as

x + x = 180

So we get

2x = 180

By division we get

x = 180/2

x° = 90°

Therefore, the measure of an angle which is equal to its complement is 90°