Question

Find Missing Angles Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
4 of 54 of 5 Items



Question
Together, the measures of ∠B
, ∠C
, and ∠D
equal 180°
. The angles have the following measures: m∠B=25°
, m∠C=(3x)°
, and m∠D=(3x+5)°
. What are the measures of ∠C
and ∠D
?(1 point)
m∠C=
°

m∠D=
°

Remaining Attempts : 3
Skip to navigation

Answer 1

To find the measures of angles \( ∠C \) and \( ∠D \), we start with the information provided:

- \( m∠B = 25° \)
- \( m∠C = (3x)° \)
- \( m∠D = (3x + 5)° \)

Since the sum of the three angles equals 180°, we can set up the following equation:

\[
m∠B + m∠C + m∠D = 180°
\]

Substituting the measures we have:

\[
25° + (3x)° + (3x + 5)° = 180°
\]

Combining like terms:

\[
25° + 3x + 3x + 5° = 180°
\]
\[
25° + 5° + 6x = 180°
\]
\[
30° + 6x = 180°
\]

Now, we can isolate \( 6x \):

\[
6x = 180° - 30°
\]
\[
6x = 150°
\]

Now, divide both sides by 6:

\[
x = 25°
\]

With the value of \( x \), we can now find \( m∠C \) and \( m∠D \):

1. For \( m∠C = 3x \):
\[
m∠C = 3(25°) = 75°
\]

2. For \( m∠D = 3x + 5 \):
\[
m∠D = 3(25°) + 5° = 75° + 5° = 80°
\]

Thus, the measures of the angles are:

- \( m∠C = 75° \)
- \( m∠D = 80° \)

In summary:
- **m∠C = 75°**
- **m∠D = 80°**