Question

If measure of two complementary angles are two consecutives even integers, then findvthe measure of the smaller angle.

Answer 1

✬ Smaller Angle = 46° ✬

Step-by-step explanation:

Given:

• Measure of two complementary angles are 2 consecutive even integers.

To Find:

• What is the measure of smaller angle ?

Solution: Let the first consecutive even integer be x. Therefore, second will be

➟ Second = x + 2

[ Complementary angles ]

• Two angles whose sum is equal to 90°.

Here we have

• First angle = x
• Second angle = x + 2

$\implies{\rm }$ x + x + 2 = 90°

$\implies{\rm }$ 2x + 2 = 90°

$\implies{\rm }$ 2x = (90 – 2)°

$\implies{\rm }$ 2x = 88°

$\implies{\rm }$ x = 88°/2

$\implies{\rm }$ x = 44°

So we got that angles

• First one is 44°
• Second is 44 + 2 = 46°

On comparing both

➬ First < Second

Hence,measure of smaller angle is of 46°.

[ Supplementary angles ]

• Two angles whose sum is equal to 180°.

Answer 2

Step-by-step explanation:

Given :

• If measure of two complementary angles are two consecutives even integers,

To Find :

• find the measure of the smaller angle.

Solution :

The sum of two complementary angles is = 90

let the two consecutive even integer be x

therefore ,x + (x + 2) = 90

According to the Question :

2x + 2 = 90

2x = 90 - 2

2x = 88

x = 88 /2

x = 44

so, as it is said to get the two consecutive even interger you got 46 as after 44 it is the consecutive even integer

x + 2

44 + 2

46

Verification :

x + (x + 2) = 90

Substitute all values :

44 + 44 + 2 = 90

44 + 46 = 90

90 = 90

Ans is 44 ,46 are the two consecutive even interger.