Question

PLS HELP 50 POINTS

In the figure shown, which pair of angles must be complementary?

A. ∠AXD and ∠DXC

B. ∠AXY and ∠YXB

C. ∠DXC and ∠BXC

D. ∠AXB and ∠BXC

Answer 1

What can you see in image?

• A co-ordinate plane
• AC a straight line

This is enough to find ans

Now

• <axb and <axc are linear pairs so their sum is 180°

One angle is 90° so other must be 90

• Complementary angles are of 90°

Hence.

• <axd and <dxc are complementary

Answer 2

`B. \text{ } \angle AXY \text{ and } \angle YXB`

Skills needed: Angle Geometry

Explanation:

1) We are given a diagram and are asked about complementary angles.

We must fully understand this term prior to solving this problem.

---> Complementary angles are angles that add up to a measure of 90 degrees. Essentially, two complementary angles make up a right angle.

2) Let's find all right angles in the diagram.

-->
`\angle BXC` is the only marked right angle, but there are 3 others.

`\angle {BXD}` is a straight angle, since
`\overline{BD}` is a straight line.

---> A straight angle has a measure of
`180\textdegree`.

`\angle BXC + \angle CXD = \angle BXD` as seen in the diagram.

Given
`\angle BXC` is 90 degrees (since it's a right angle), and
`\angle{BXD}` is 180 degrees (since it's a straight angle), we can solve for
`\angle{CXD}`

`90+ \angle CXD =180 \\ \angle CXD=90`

This means ANGLE CXD is a right angle.

We can do this process 2 more times. Using the fact that
`\overline{CA}` is a straight line (so
`\angle CXA = 180\textdegree`), we can determine that
`\angle{BXA}` and
`\angle{DXA}` are both right angles.

3) Now let's see if there are any two angles that combine to make a right angle.

`\angle{BXC}, \angle{DXC}, \text{ and } \angle{DXA}` all are not split.

`\angle{BXA}` however, is split into two angles (
`\angle{YXB}\text{ and } \angle AXY`

These two angles would be complementary as they make up a right angle.
`B` is the answer.