Question

Two angle are complementary to
each other. If the measure of one
of them is 4 times that of the
other. Find the measures of the
angle.​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The angles are 18° and 72°.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

The angles are = Complementary Angles

One Angle = 4 times that of the

other.

To Find :

The measures of the angle.

Solution :

◆ $\textbf{\small{\underline{Consider the -}}}$

• One Angle as x
• Second Angle as 4x

Complementary Angles are the angles which sum up and make 90°.

⛤ x + 4x = 90

$\longrightarrow \: x + 4x = 90$

$\longrightarrow \: 5x = 90$

$\longrightarrow \: x = \dfrac{90}{5}$

$\longrightarrow \: x = 18$

$\rule{300}{1.5}$

★ Value of 4x

$\longrightarrow \: 4 \times 18$

$\longrightarrow \: 72$

One Angle = 18°

Second Angle = 72°

$\therefore$ The angles are 18° and 72°.

$\rule{300}{1.5}$

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

$\longrightarrow$ 72 + 18 = 90

$\longrightarrow$ 90 = 90

$\therefore$ The angles are 18° and 72°.

Answer 2

Answer -

Let one angle be as x and another one be as 4x

==> x + 4x = 90° ..........[Complementary angles' sum is 90°]

==> 5x = 90

==> x = 90/5

==> x = 18

4x = 4 × 18 = 72°

.°. The angles are 18° and 72°