Two angles are complementary. One angle has a measure of and the other has a measure of .

Question

What is the value of ? (1 point)
40° (8x + 2) °
x
6
11
60
50

Answer 1

Since two angles are complementary, their measures add up to 90 degrees. Let's call the measure of one angle x. Then the measure of the other angle is 90 - x.
According to the problem, the two angles have measures of 40° (8x + 2) and x. So we can set up an equation:
(8x + 2) + x = 90
Combining like terms:
9x + 2 = 90
Subtracting 2 from both sides:
9x = 88
Dividing both sides by 9:
x = 88/9
Since the answer choices are whole numbers, we can approximate x. Dividing 88 by 9 gives us approximately 9.77. Therefore, x is closest to 9.
So the value of x is approximately 9. Now we can substitute this value back into the equation to find the measure of the two angles:
(8x + 2) + x = 90
(8(9) + 2) + 9 = 90
(72 + 2) + 9 = 90
74 + 9 = 90
83 = 90
This equation is not true. Therefore, the given information is invalid and we cannot determine the value of the angle. None of the answer choices are correct.

Answer 2

which option is correct

Answer 3

Apologies for the incorrect response earlier. Let's solve the problem correctly:

Let's call the measure of one angle x. Then the measure of the other complementary angle is 90 - x.

According to the problem, one angle has a measure of 40° (8x + 2) and the other angle has a measure of x.

Setting up an equation:
40° (8x + 2) + x = 90

Simplifying the equation:
320x + 80 + x = 90
321x + 80 = 90
321x = 10
x = 10/321

Therefore, the value of x is 10/321. Since this value is not a whole number, none of the answer choices provided are correct.