Question

The m∠B is 93°, mBC is 58°, and mCD is 106°. Find the missing angle measures.

(2 points)
m∠A=
°, m∠C=
°, and m∠D=
°

Answer 1

To find the missing angle measures, we can use the information given regarding the angles in triangle ABCD.

Given:
- \( m∠B = 93° \)
- \( m∠BC = 58° \) (presumably this is an angle made with segment BC)
- \( m∠CD = 106° \)

We start by calculating the angles in triangle ABCD:

1. We know that the sum of the angles in a triangle is \( 180° \). If we assume that angles A, B, and C are part of the same triangle, we can write:

\[
m∠A + m∠B + m∠C = 180°
\]

Substituting the values we have:

\[
m∠A + 93° + 58° = 180°
\]

This simplifies to:

\[
m∠A + 151° = 180°
\]

Now we can solve for \( m∠A \):

\[
m∠A = 180° - 151° = 29°
\]

2. Next, to find m∠C, we can use the information regarding m∠CD. In a straight line configuration involving points C and D, if angles C and CD are angles on a straight line, then:

\[
m∠C + m∠CD = 180°
\]

Substituting for m∠CD:

\[
m∠C + 106° = 180°
\]

Simplifying gives:

\[
m∠C = 180° - 106° = 74°
\]

3. Finally, angle D can be calculated as follows. If angles A, C, and D form another triangle, we have:

\[
m∠A + m∠C + m∠D = 180°
\]

Substituting the known values:

\[
29° + 74° + m∠D = 180°
\]

This gives:

\[
m∠D = 180° - 103° = 77°
\]

Putting it all together:

- \( m∠A = 29° \)
- \( m∠C = 74° \)
- \( m∠D = 77° \)

So the final answers are:

- \( m∠A = 29° \)
- \( m∠C = 74° \)
- \( m∠D = 77° \)