Question

If an angle is 45° more than half of its complement, find the measure of the angle

Answer 1

Answer:

60 degree..

Step-by-step explanation:

Let us assume that the angle is x.

Then,its complement will be 90-x.

45 degree more than one half of its complement

i.e 45+(90-x)/2

According to the sum,

x=45+(90-x)/2

x=90+90-x/2

x=180-x/2

2x=180-x

3x=180

x=60.

Hence the angle is 60

Answer 2

Given  : an angle is 45° more than half of its complement,

To Find :  the measure of the angle

Solution:

complementary angles add up to 90 degrees (a Right Angle).

Let say Angle be  A

then its complement = 90 - A

Half of complement = (1/2)(90 - A) = 45 - A/2

angle is 45° more than half of its complement,

=> A = 45 + 45 - A/2

=> 3A/2 = 90

=> 3A = 180

=> A = 60

Angle is 60°

Verification

Angle = 60°

Complement = 30°

Half of complement = 15°

15° + 45° = 60°

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