Answer: 56° and 34°
Step-by-step explanation: Well we know this is a complementary angle and if two angles are complementary, then the sum of their measures is 90 degrees.
If these two angles have to add together to be 90 degrees, we can use that fact to set up our equation. We can say that 4x + (2x + 6) = 90.
Simplifying from here, we have 6x + 6 = 90.
Subtracting 6 from both sides, we have 6x = 84.
Dividing both sides by 6, we find that x = 14.
Now, remember that these should add up to 90 degrees.
We can check by substituting the value that we just found back in for x to check our angles. If they add to 90 degrees, we did it correctly.
So for the first one we have 4(14) which is 56 and for the next one we have 2(14) + 6 or 28 + 6 which simplifies to 34.
Now adding, 56 + 34 gives us 90.
So, we know that these are the correct measures.