+394 Use the diagram to find the measure of exterior angle BCD.
Triangle A B C has angles labeled as follows: A, (18x + 12) degrees; B, 6x degrees; C, unlabeled. Point C lies on Ray A D. The outside angle B C D is labeled (27x - 3) degrees.
left parenthesis 27 x minus 3 right parenthesis degrees(27x − 3)°
6 x degrees6x°
left parenthesis 18 x plus 12 right parenthesis degrees(18x + 12)°
DCAB
The measure of exterior angle BCD is ___
+9466 m∠BCA + m∠BCD = 180
m∠BCA = 180 - m∠BCD
m∠BCA = 180 - (27x - 3)
the sum of the angles in a triangle = 180°
6x + (18x + 12) + m∠BCA = 180
6x + (18x + 12) + (180 - (27x - 3)) = 180
6x + 18x - 27x + 12 + 180 + 3 = 180
-3x = -15
x = 5
m∠BCD = (27x - 3)°
m∠BCD = (27(5) - 3)°
m∠BCD = 132°
+9466 m∠BCA + m∠BCD = 180
m∠BCA = 180 - m∠BCD
m∠BCA = 180 - (27x - 3)
the sum of the angles in a triangle = 180°
6x + (18x + 12) + m∠BCA = 180
6x + (18x + 12) + (180 - (27x - 3)) = 180
6x + 18x - 27x + 12 + 180 + 3 = 180
-3x = -15
x = 5
m∠BCD = (27x - 3)°
m∠BCD = (27(5) - 3)°
m∠BCD = 132°
