Question

Quadrilateral ABCD is a parallelogram. Determine the measure of Angle A

Answer 1

Answer:

$\huge\boxed{\text{(A)}\ 96 \textdegree}$

Step-by-step explanation:

A parallelogram has two pairs of identical angles.

The identical angles will be directly opposite from each other.

This means that:

• Angle C = Angle A
• Angle D = Angle B

Therefore, we can say that Angle A is 3x degrees and Angle B is x+52 degrees.

It's also important to note that all angles in a quadrilateral add up to 360°.

Since we know the measure of each angle, we can add up the expressions for each and find x.

$3x + 3x + (x+52) + (x+52) = 360$

Let's simplify this equation.

• $6x+(x+52)+(x+52)=360$
• $8x+104=360$

• $8x=256$

• $x=32$  

Now that we know the value of x, let's use it to find the measure of Angle A.

We already proved earlier that Angle C is equivalent to Angle A. Since we know the expression for Angle C (3x) it'll be the same for angle A.

$3(32)=96$

So A is 96°

Hope this helped!