Answer:
x = 45°, y = 53°, z = 82°
Step-by-step explanation:
x is the first angle, y is the second, and z is the third.
The sum of the second and third, which is denoted by y + z, is 3 times the measure of the first, which is just x. So, we have:
y + z = 3 * x
Additionally, the third angle, z, is 29 more than the second, y, so:
z = 29 + y
We also know that the sum of the three is 180, so:
x + y + z = 180
Let's substitute y + z in the last equation with 3 * x:
x + y + z = 180
x + 3x = 180
4x = 180
x = 45
Now, we know that y + z = 3 * 45 = 135. We also know that z = 29 + y, so substitute 29 + y in for z in y + z = 135:
y + z = 135
y + (29 + y) = 135
2y + 29 = 135
2y = 106
y = 53
Finally, use this value of y to solve for z:
z = 29 + y
z = 29 + 53 = 82
Thus, the angles are x = 45°, y = 53°, and z = 82°.
<em>~ an aesthetics lover</em>
