Question

An angle is twice as large as its complement. What is the measure of the angle and its complement?

Answer 1

Hint: In this question, we need to find the angle and its complement angle. Given that an angle is twice of its complement. Geometrically, two angles are said to be complementary angles if their sum is \[90^{o}\]. In some cases, they form a right angled triangle. Here We need to find the angle and its complement. We can assume the angle by a variable, then as per the given the complement is twice the angle. First we need to form an expression as the question says. Then by solving, we can find the value of the angle and its complement.

Complete step-by-step solution:
Let us assume the angle is \[x\]. Given that the complement is twice of the angle. That is the complement is \[2x\].

We also know that two angles are said to be complementary angles if their sum is \[90^{o}\].
\[\Rightarrow x+2x=90^{o}\]
By adding, we get,
\[\Rightarrow 3x=90^{o}\]
\[\Rightarrow x=\dfrac{(90^{o})}{3}\]
On simplifying, we get,
\[x=30^{o}\]
Thus we get the angle as \[30^{o}\]. Now we can find the complement of the angle which \[2x\].
\[\Rightarrow 2\times (30^{o})\]
On multiplying, we get,
The complement angle as \[60^{o}\].
The angle and its complement are \[30^{o}\] and \[60^{o}\] respectively.

Note: We can also check whether our answer is correct or not. We know that two angles are said to be complementary angles if their sum is \[90^{o}\]. If the sum of the angle and the complement is \[90^{o}\] then our answer is absolutely correct. A simple example for the complementary angles are \[50^{o}\] and \[40^{o}\].Similarly, two angles are said to be supplementary angles if their sum is \[180^{o}\]. A simple example for supplementary angles are \[160^{o}\] and \[20^{o}\].