Question

The measure of ZA is 12° greater than the measure of ZB. The two angles are complementary. Find the measure of each angle.

Answer 1

The measurement of angle A is 12 greater than angle B

So, angle A > angle B

Angle A = 12 + angle B

`\angle A=12+\angle B`

The two angles are complementary angles:

The sum of pair of complementary angle is 90

So,

`\angle A+\angle B=90`

Let angle A = xang angle B as y

So, equation : x = 12 + y, x + y = 90

Substitute the expression of x =12 +y in the second equation

`\begin{gathered} x+y\text{ = 90} \\ 12+y+y=90 \\ 12+2y=90 \\ 2y=90-12 \\ 2y=78 \\ y=(78)/(2) \\ y=39 \end{gathered}`

Now, put y =39 in the first equation,

`\begin{gathered} x=12+y \\ x=12+39 \\ x=51 \end{gathered}`

So, x = 51 and y =39

thus,

`\begin{gathered} x=m\angle A=51 \\ y=m\angle B=39 \end{gathered}`

The measurement of all angle is 51 & 39

Answer: Angle A = 51, Angle B = 39