Respuesta :
The measurement of angle A is 12 greater than angle B
So, angle A > angle B
Angle A = 12 + angle B
[tex]\angle A=12+\angle B[/tex]The two angles are complementary angles:
The sum of pair of complementary angle is 90
So,
[tex]\angle A+\angle B=90[/tex]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
[tex]\begin{gathered} x+y\text{ = 90} \\ 12+y+y=90 \\ 12+2y=90 \\ 2y=90-12 \\ 2y=78 \\ y=\frac{78}{2} \\ y=39 \end{gathered}[/tex]Now, put y =39 in the first equation,
[tex]\begin{gathered} x=12+y \\ x=12+39 \\ x=51 \end{gathered}[/tex]So, x = 51 and y =39
thus,
[tex]\begin{gathered} x=m\angle A=51 \\ y=m\angle B=39 \end{gathered}[/tex]The measurement of all angle is 51 & 39
Answer: Angle A = 51, Angle B = 39
