Supplementary angles are two angles whose measures add up to 180 degrees. We are given the measures of the angles as ∡ACB = (x + 28)° and ∡BCD = (x + 48)°.
To find the value of \( x \), we can set up the equation:
\[ (x + 28)° + (x + 48)° = 180° \]
Combine the \( x \) terms and the constants:
\[ 2x + 76 = 180 \]
Subtract 76 from both sides:
\[ 2x = 104 \]
Next, divide both sides by 2:
\[ x = 52 \]
Now, substitute \( x = 52 \) back into \( ∡BCD = (x + 48)° \):
\[ ∡BCD = (52 + 48)° = 100° \]
Therefore, the measure of ∡BCD is:
\[ 100° \]
∠ACB
and ∠BCD
are supplementary angles. The angles have the following measures: ∡ACB=(x+28)°
and ∡BCD=(x+48)°
. What is m∠BCD
?(1 point)
Responses
100°
100 degrees
128°
128 degrees
52°
52 degrees
80°
1 answer
16 answers