Question

Two complementary angles are such that one is 14° more than three times the second angle. What is the measure of the larger angle?

Answer 1

Answer:-

Larger angle = 71°

Smaller angle = 19°

Explanation:-

Given:

Two complementary angles, such that one angle is 14° more than three times the second angle

To Find:

Measure of larger angle

Solution:

Let,

• larger angle be x
• Smaller angle be y

since, they are complementary..

x + y = 90° ----(1)

acc. to the question:

x = 14° + 3y -----(2)

Put, eq. (2) in (1)

14° + 3y + y = 90

4y = 90-14

4y = 76°

•°• y = 19°

Now,

x = 14° + 3y

x = 14° + 3(19)

x = 14° + 57

•°• x = 71°

Verification:-

X + Y = 90

71° + 19° = 90°

90° = 90°

Hence, 71° and 19° are the angles

Answer 2

Given:

Two complementary angles, such that one angle is 14° more than three times the second angle

To Find:

Measure of larger angle

Let,

larger angle be x

Smaller angle be y

since, they are complementary

x + y = 90° ----(1)

acc. to the question:

x = 14° + 3y -----(2)

Put, eq. (2) in (1)

14° + 3y + y = 90

4y = 90-14

4y = 76°

y = 19°

Now,

x = 14° + 3y

x = 14° + 3(19)

x = 14° + 57

x = 71°