Question

Find the measure of the angle which is:
a) one - fourth of its supplement
b) double of its complement.
Note: Show required working in each part.

Answer 1

Answer:

Let the required angle be x.

Its complement =(90−x) & its supplement =(180−x).

Given that, Its complement =

4

1

of its supplement.

⇒(90−x)=

4

1

×(180−x)

⇒360−4x=180−x

⇒4x−x=360−180

⇒3x=180

⇒x=

3

180

⇒x=60

o

Answer 2

Answer:

Let x be the angle.

The complement of the angle is 90

∘

−x.

The supplement of the angle is 180

∘

−x.

According to the question,

90

∘

−x=

4

1

(180

∘

−x)

4(90

∘

−x)=180

∘

−x

360

∘

−4x=180

∘

−x

360

∘

−180

∘

=3x

180

∘

=3x

x=60

∘

Step-by-step explanation:

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