Question

Two complementary angles are in the ratio 2:3 find the measure of the larger angle

Answer 1

As we know that complementary angles measure 90 degrees.
Let the common ratio be x
Then..
2x+3x=90
5x=90
x=18
So the angles will measure..
36 degree and 54 degree

54 degree is the measure of the larger angle

Answer 2

Answer:

Required larger angle is ${54}^{o}$

Step-by-step explanation:

Here given two Complementary angles are 2:3.

Let first Complementary angle be 2x and second complementary angle be 3x.

Here we want to find larger angle.

Now question is what is Complementary angle?

We know if sum of two angles is equal to 90° then they are called Complementary angle.

By some example,we can understand this concept easily.

Example -1:

Two angles are 30° and 60°

Sum of these two angles

$= {30}^{o} + {60}^{o} = {90}^{o}$

Example -2:

Two angles are 10° and 80°

Sum of these two angles

$= {10}^{o} + {80}^{o} = {90}^{o}$

According to question,

$2x + 3x = {90}^{o} \\ 5x = {90}^{o} \\ x = \frac{ {90}^{o} }{5} = {18}^{o}$

First angle is $(2 \times {18}^{o} ) = {36}^{o}$

Second angle is $(3 \times {18}^{o} ) = {54}^{o}$