Question

question 5
given abcd is a parallelogram, solve for x.
(30 + 5x)° (15 + 10x)°
13
9
11
7

Explanation:

Step1: Recall parallelogram angle property

In a parallelogram, consecutive angles are supplementary (sum to \(180^\circ\)). So, \(\angle A + \angle D = 180^\circ\).

Step2: Set up the equation

Substitute the given angle expressions: \((30 + 5x) + (15 + 10x) = 180\).

Step3: Simplify the left - hand side

Combine like terms: \(30+15 + 5x+10x=180\), which simplifies to \(45 + 15x=180\).

Step4: Solve for x

Subtract 45 from both sides: \(15x=180 - 45=135\). Then divide both sides by 15: \(x=\frac{135}{15}=9\).

Answer:

9