Question

parallelograms
given that the quadrilateral shown is a parallelogram. use the properties of parallelograms to find x if ∠a = 133° and ∠d = (3x + 35)°.
a x = 2
b x = 4
c x = 5
d x = 7
use the properties of parallelograms to find x if ∠a = 122° and ∠c = (2x + 60)°
a x = 27
b x = 29
c x = 31
d x = 33

Explanation:

First Sub - Question (∠A = 133° and ∠D=(3x + 35)°)

Step1: Recall property of parallelogram

In a parallelogram, consecutive angles are supplementary (sum to 180°). So, ∠A+∠D = 180°.

Step2: Substitute values and solve

Substitute ∠A = 133° and ∠D=(3x + 35)° into the equation:
\(133+(3x + 35)=180\)
Simplify the left - hand side: \(168 + 3x=180\)
Subtract 168 from both sides: \(3x=180 - 168=12\)
Divide both sides by 3: \(x = \frac{12}{3}=4\)

Second Sub - Question (∠A = 122° and ∠C=(2x + 60)°)

Step1: Recall property of parallelogram

In a parallelogram, opposite angles are equal. So, ∠A = ∠C.

Step2: Substitute values and solve

Substitute ∠A = 122° and ∠C=(2x + 60)° into the equation:
\(2x+60 = 122\)
Subtract 60 from both sides: \(2x=122 - 60 = 62\)
Divide both sides by 2: \(x=\frac{62}{2}=31\)

Answer:

First sub - question: B. \(x = 4\)
Second sub - question: C. \(x = 31\)