Question

Two angles are complementary. If the larger angle is twice the measure of the smaller angle, then find the value of the smaller angle.
a) \[{{30}^{0}}\]
b)\[{{45}^{0}}\]
c) \[{{60}^{0}}\]
d) \[{{15}^{0}}\]

Answer 1

Hint: To solve the question, we have to mathematically represent the statement which states that the larger angle and smaller angle are complementary. The given relation between larger angle and smaller angle will ease the procedure of solving.

Complete step by step solution:
Let \[{{x}^{0}},{{y}^{0}}\] be the larger angle and smaller angle respectively.

We know that two angles are complementary when the sum of the angles is equal to \[{{90}^{0}}\].

This implies that the sum of the larger angle and smaller angle is equal to \[{{90}^{0}}\].
\[{{x}^{0}}+{{y}^{0}}={{90}^{0}}\] …… (1)

Given that the larger angle is twice the measure of the smaller angle, which implies
\[{{x}^{0}}=2{{y}^{0}}\]

By substituting the above equation in equation (1), we get

\[2{{y}^{0}}+{{y}^{0}}={{90}^{0}}\]

\[3{{y}^{0}}={{90}^{0}}\]

\[{{y}^{0}}=\dfrac{{{90}^{0}}}{3}\]

\[\Rightarrow {{y}^{0}}={{30}^{0}}\]

Thus, the value of the smaller angle is equal to \[{{30}^{0}}\]

Hence, option (a) is the right choice.

Note: The possibility of mistake can be not able to analyse that complementary angles implies the sum of the angles is equal to \[{{90}^{0}}\]. The possibility of mistake can happen when they mistake complementary angles which implies the sum of the angles is equal to \[{{90}^{0}}\] as supplementary angles which implies the sum of the angles is equal to \[{{180}^{0}}\] . The confusion may occur due the rhyming words. The alternate way to solve the question by checking the options whether they satisfy the condition that the larger and smaller angles are complementary. Thus, we can eliminate the options to arrive at the right choice.