Question

solve for x.
(the image shows a parallelogram abcd with angle at b being (2x + 15)° and angle at c being x°. the options are 180, 115, 55, 82.5)

Explanation:

Step1: Identify the property of a parallelogram

In a parallelogram, consecutive angles are supplementary, meaning they add up to \(180^\circ\). So, \(\angle B + \angle C = 180^\circ\).

Step2: Set up the equation

Substitute the given angles: \((2x + 15) + x = 180\).

Step3: Solve the equation

Combine like terms: \(3x + 15 = 180\).
Subtract 15 from both sides: \(3x = 180 - 15 = 165\).
Divide both sides by 3: \(x = \frac{165}{3} = 55\).

Answer:

55