Question

Problem

What is the relationship between
∠a\blueD{\angle a}
∠a
start color #11accd, angle, a, end color #11accd
and
∠b\greenD{\angle b}
∠b
start color #1fab54, angle, b, end color #1fab54
?

Answer 1

supplementary angles

Explanation:

Answer 2

Complementary angles.

Explanation:

The graph is attached.

Notice that
`\angle a=\angle AXY`,
`\angle b = \angle YXB` and
`\angle BXC = 90\°`, by given.

`\angle AXB = \angle AXY + \angle YXB`, by sum of angles.

`\angle AXB + \angle BXC = 180\°`, by supplementary angles definition.

`\angle AXB + 90\° = 180\°\\\angle AXB = 180\° - 90\°\\\angle AXB = 90\°`

Which means,

`\angle AXB = \angle AXY + \angle YXB = 90\°`

Therefore,
`\angle a + \angle b = 90\°`, in other words, angles a and b are complementary by defintion.

So, the right answer is the second choice.