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)
• 52°
• 100°
• 67°
• 80°
To find the measure of BCD, we can set up an equation using the given information. We know that the sum of the three angles is 180°:
m ACB + m BCD + m DCE = 180°
Substituting the given angle measures, we have:
(x + 15)° + (x + 48)° + 13° = 180°
Combining like terms, we get:
2x + 76° = 180°
Subtracting 76° from both sides, we have:
2x = 104°
Dividing both sides by 2, we find:
x = 52°
Now that we have the value of x, we can find the measure of BCD:
m BCD = x + 48° = 52° + 48° = 100°
Therefore, the measure of BCD is 100°. Answer choice: 100°.