Two adjacent angles of a parallelogram are (3x − 4)° and (3x + 10)° then the…
2022
Two adjacent angles of a parallelogram are (3x − 4)° and (3x + 10)° then the smaller angle of the parallelogram is -
- A.
83°
- B.
89°
- C.
97°
- D.
106°
Attempted by 10 students.
Show answer & explanation
Correct answer: A
Step-by-Step Solution
Set up the equation: Since the angles are (3x - 4) and (3x + 10), their sum is 180:
(3x - 4) + (3x + 10) = 180
Simplify and solve for x:
6x + 6 = 180
6x = 174
x = 174 / 6
x = 29
Find the two angles:
Angle 1: 3(29) - 4 = 87 - 4 = 83 degrees
Angle 2: 3(29) + 10 = 87 + 10 = 97 degrees
Identify the smaller angle: Comparing 83 degrees and 97 degrees, the smaller angle is 83 degrees.