Question

two adjacent angles are on a straight line one angle has a measure of (5x - 28) ∘ and the other angle has a measure of (8x) ∘ what is the measure of the second angle

A: 52 ∘

B: 120 ∘

C: 16

D: 128
Answer
For two adjacent angles with measures x ∘ and (x + 30) ∘ that make up a 90 ∘ angle what is x?

A: 30

B: 15

C: 60

D: 20
Answer
A right angle is formed by two adjacent angles with measure of (x) ∘ and (x + 30) ∘ what are the two angles measures

A: 70 ∘ and 25 ∘

B: 30 ∘ and 60

C: 75 and 105

D: 60 ∘ and 90
Answered by GPT 3.5
Since the angles are adjacent and on a straight line, they add up to 180 degrees.

So, (5x - 28) + (8x) = 180.

Combining like terms, 13x - 28 = 180.

Adding 28 to both sides, 13x = 208.

Dividing both sides by 13, x = 16.

Substituting x = 16 into the expression for the second angle, we find (8x) = (8 * 16) = 128.

Therefore, the measure of the second angle is 128 degrees, which corresponds to option D.
Answered by GPT 3.5
Since two adjacent angles make up a 90 degree angle, we have the equation x + (x + 30) = 90.

Combining like terms, we get 2x + 30 = 90.

Subtracting 30 from both sides, we have 2x = 60.

Dividing both sides by 2, we find x = 30.

Therefore, x = 30, which corresponds to option A.
Answered by GPT 3.5
In a right angle, the two adjacent angles are complementary, meaning their measures add up to 90 degrees.

So, we have the equation x + (x + 30) = 90.

Combining like terms, we get 2x + 30 = 90.

Subtracting 30 from both sides, we have 2x = 60.

Dividing both sides by 2, we find x = 30.

Therefore, the two angle measures are x = 30 degrees and (x + 30) = 30 + 30 = 60 degrees.

Thus, the correct answer is option B: 30 degrees and 60 degrees.