Question

In a triangle, the measure of the first angle is twice the measure of the second angle. The measure of third angle os 88 degrees more then the measure of the second angle. Use the fact that the sum of the measures of the three angles of a triangle is 180 to find the measures of each angle.

Answer 1

Answers: 46, 23, and 111

Explanation:

To answer, we need to know the angles. Therefore, give each angle a name. Angle 1 will be x, 2 will be y, 3 will be z. So, using this system of equations:

x=2y

z=y+88

x+y+z=180

Substituting, z = 1/2(x)+88, now plug z into the third equation:

x+1/2(x)+1/2(x)+88=180

this simplifies to 2x+88=180

subtracting 88 from both sides leaves 2x=92

x=46

plug this in to the first equation: 46 = 2y, so y = 23

plug this into the third one leaves z = 111

Hope this helps!