Question

The sum of the measures of two complementary angles is 90 degrees. If one angle measures 3 degrees more than twice the measure of the other, find the measure of the smaller angle

Answer 1

Answer: 30 then 30 x 2 = 60

Answer 2

Answer:

If one angle measures 3 degrees more than twice the measure of the other.The measure of smaller angle is 29°

Solution:

Consider “a” as the measure of smaller angle and “b” as the measure of compliment of second angle.

Given that one angle measures 3 degrees more than twice the measure of other. Hence we consider angle “y” measures 3 degrees more than twice the other angle “x”

y = 3 + 2x --- eqn 1

Given that, sum of complimentary angles is 90° .hence we get,

x + y = 90 --- eqn 2

Substituting eqn1 in eqn 2, we get  

x + 3 + 2x = 90

on rearranging and solving for “x” , we get

3x + 3 = 90

3x = 90-3

3x = 87

$x = \frac{87}{3} = 29$

On substituting x=29 in eqn 1,we get the value of y

y = 3 + 2 (29) = 3 + 58 = 61

Hence we get “x” = 29 and “y” =  61 .So the measure of smaller angle is 29°