Answer:
-41 degrees
Step-by-step explanation:
If angle a is complementary to angle b, it means that the sum of the measures of these two angles equals 90 degrees (because complementary angles add up to 90 degrees). So, you can set up the equation:
Angle a + Angle b = 90 degrees
Given that angle b equals 3x - 410 and angle a equals x + 8, you can substitute these expressions into the equation:
(x + 8) + (3x - 410) = 90
Now, simplify and solve for x:
4x - 402 = 90
Add 402 to both sides:
4x = 90 + 402
4x = 492
Now, divide both sides by 4 to isolate x:
x = 492 / 4
x = 123
So, x equals 123. Now that you've found the value of x, you can find the measures of angle a and angle b:
Angle a = x + 8 = 123 + 8 = 131 degrees
Angle b = 3x - 410 = 3(123) - 410 = 369 - 410 = -41 degrees