Three angles measures add to 180°
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
80°
80 degrees
67°
67 degrees
52°
To find the measure of ∠BCD, we need to set up an equation using the fact that the sum of the three angles is 180°.
m∠ACB + m∠BCD + m∠DCE = 180°
Substituting the given measures,
(x+15)° + (x+48)° + 13° = 180°
Combining like terms,
2x + 76° + 13° = 180°
2x + 89° = 180°
Subtracting 89° from both sides,
2x = 91°
Dividing both sides by 2,
x = 45.5°
Now we can find the measure of ∠BCD:
m∠BCD = x + 48°
m∠BCD = 45.5° + 48°
m∠BCD = 93.5°
Therefore, the measure of ∠BCD is 93.5°.
wrong
Apologies for the error. Let's try solving it again:
The sum of the three angles is 180°:
m∠ACB + m∠BCD + m∠DCE = 180°
Substituting the given measures:
(x+15)° + (x+48)° + 13° = 180°
Combining like terms:
2x + 76° + 13° = 180°
2x + 89° = 180°
Subtracting 89° from both sides:
2x = 91°
Dividing both sides by 2:
x = 45.5°
Now we can find the measure of ∠BCD:
m∠BCD = x + 48°
m∠BCD = 45.5° + 48°
m∠BCD = 93.5°
Therefore, the measure of ∠BCD is 93.5°.
still wrong pick one of the responses
Apologies for the continued error. Let's try picking one of the responses:
Given the measures of ∠ACB and ∠DCE, we can find the measure of ∠BCD by subtracting the sum of the other two angles from 180°:
∠BCD = 180° - (∠ACB + ∠DCE)
∠BCD = 180° - ((x+15)° + 13°)
Simplifying:
∠BCD = 180° - (x + 15° + 13°)
∠BCD = 180° - (x + 28°)
Since we don't have the value of x, we can't determine the exact measure of ∠BCD. Therefore, we cannot determine which of the given options (100°, 80°, 67°, 52°) is correct without knowing the value of x.