geometry measure of an angle

Question

The measure of angle X is 18 more than 3 times the measure of its complement. Find the measure of angle X.

Answer 1

Sum of complementary angles is 90°.

 

Thus if complement of angle X measures mº , then measure of angle X is =18º+3mº

 

We have,

18º+3 mº +  mº = 90°

=>4mº+18º= 90° ........... adjusting operators annd coefficients

=>4mº= 90°-18º .......... subtracting 18º from both sides

=>4mº=72° ........... adjusting operators

=>mº=18° ........... dividing both sides by 4 ----------------- (1)

 

Thus,  measure of angle X is =18º+3mº = 18º+3*18° ...... substituting mº=18° from (1)

                                                          =18º+54º

                                                          =72°

Hence measure of angle X is 72°.

Answer 2

If X is the measure of the angle, then 90 - X is the measure of its complement.

 

The problem translates to the equation:

 

X = 18 + 3(90 - X).

 

You must solve this for X:

 

X = 18 + 270 - 3X

4X = 288

X = 288/4 = 72

 

The angle measures 72°.