Solve Equations with Supplementary Angles Quick Check
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Question
Three angles measures add to 180°
and have the following measures: m∠ACB=(x+15)° , m∠BCD=(x+48)° , and m∠DCE=13° . What is the measure of ∠BCD ?(1 point)
Responses
100°
100 degrees
67°
67 degrees
80°
80 degrees
52°
52 degrees
To find the measure of angle BCD, we can use the fact that the sum of the three angles is equal to 180°.
So, we have the equation: (x+15) + (x+48) + 13 = 180°
Combining like terms, we get: 2x + 76 = 180°
Subtracting 76 from both sides, we get: 2x = 104°
Dividing both sides by 2, we get: x = 52°
Therefore, the measure of angle BCD is x+48 = 52°+48° = 100°.
So, the correct answer is: 100°.