Find Missing Angles Practice

Question

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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
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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°