Answer:
The equations are 4a + 2b = 360 and a + b = 116
the value of a = 64 and the value of b = 52
Step-by-step explanation:
∵ The figure is a parallelogram
∴ The sum of its angles = 360°
∴ 4a + 2b = 360°⇒ divide both sides by 2
∴ 2a + b = 180⇒(1)
∵ The measure of the largest angle is 116°
∴ a + b = 116⇒(2)
Solve the equations (1) and (2)
From equation (2) ⇒ b = 116 - a
Substitute in equation (1)
2a + 116 - a = 180
∴ a = 180 - 116 = 64
∴ b = 116 - 64 = 52
