Answer:
The measure of angle A is: m∠A = 96
Therefore, option A is true.
Step-by-step explanation:
Given
m∠C = 3x
m∠D = x+52
We know that the opposite angles of a parallelogram are also equal.
Determining m∠A
It is clear that A is the opposite angle of C.
i.e.
m∠A = m∠C
as m∠C = 3x
so m∠A = 3x
Determining m∠B
It is also clear that B is the opposite angle of D.
i.e.
m∠B = m∠D
as m∠D = x+52
so m∠B = x+52
We know that the sum of the angles of a parallelogram is 360°.
so
m∠A + m∠B + m∠C + m∠D = 360°
3x + (x+52) + 3x + (x+52) = 360°
Group like terms
[tex]3x+x+3x+x+52+52=360^{\circ \:}[/tex]
[tex]8x+104=360^{\circ \:}[/tex]
Subtract 104 on both sides
[tex]8x+104-104=360^{\circ \:}-104[/tex]
Simplify
[tex]8x=360^{\circ \:}-104[/tex]
[tex]8x=256[/tex]
Divide both sides by 8
[tex]\frac{8x}{8}=\frac{256}{8}[/tex]
Simplify
[tex]x=32[/tex]
Thus,
The measure of the angle A is:
m∠A = 3x
substitute x = 32
m∠A = 3(32)
m∠A = 96
Hence, the measure of angle A is: m∠A = 96
Therefore, option A is true.
