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 52° 52 degrees 100° 100 degrees 67° 67 degrees 80°
I Gotchyall don't worry here are the answers for the quick check:
1: 10x-20=180
2: 9x+135=180
3: 165
4: 110
5: 100
To find the measure of ∠BCD, we need to use the fact that the sum of the angles in a triangle is 180°.
The given angles are:
m∠ACB = (x+15)°
m∠BCD = (x+48)°
m∠DCE = 13°
Using the fact that the sum of the angles in a triangle is 180°, we can set up the following equation:
(x+15)° + (x+48)° + 13° = 180°
Simplifying the equation:
2x + 76° = 180°
Subtracting 76° from both sides:
2x = 104°
Dividing both sides by 2:
x = 52°
Therefore, the measure of ∠BCD is x + 48°, which is equal to 52° + 48° = 100°.
So, the measure of ∠BCD is 100°.