Question

ABCD is a parallelogram angle A=3x-2 angle C =50-x find angle A
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Answer 1

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Since opposite angles of a parallelogram are equal. Therefore,

3x−2=50−x⇒x=13

(3x−2)

∘

=3(13)−2=37

∘

The measures of the adjacent angles of a parallelogram add up to be 180 degrees, or they are supplementary.

Another angle =180−37=143

∘

The measure of each angle of the parallelogram.

37 ∘

,143 ∘

,37 ∘

,143 ∘

Answer 2

Given Information:

• ABCD is a parallelogram
• ∠A is (3x-2)°
• ∠C is (50-x)°

Need to Find:

• Measure of ∠A

Property of Parallelogram used here:

• In a parallelogram, opposite angles are equal.

Solution:

As we know, the opposite angles of parallelogram are equal. So,

$\: \: \: \: \: \: \: \: \: \longrightarrow\sf{\angle A=\angle C}$

$\: \: \: \: \: \: \: \: \: \longrightarrow\sf{{(3x-2)}^{\circ}={(50-x)}^{\circ}}$

$\: \: \: \: \: \: \: \: \: \longrightarrow\sf{3x-2=50-x}$

$\: \: \: \: \: \: \: \: \: \longrightarrow\sf{3x+x=50+2}$

$\: \: \: \: \: \: \: \: \: \longrightarrow\sf{4x=52}$

$\: \: \: \: \: \: \: \: \: \longrightarrow\sf{x=\dfrac{52}{4}}$

$\: \: \: \: \: \: \: \: \: \longrightarrow\bold{x=13}$

~Substituting value of 'x' in ∠A,

$\: \: \: \: \: \: \: \: \: \implies\sf{\angle A={(3x-2)}^{\circ}}$

$\: \: \: \: \: \: \: \: \: \implies\sf{\angle A={(3\times 13-2)}^{\circ}}$

$\: \: \: \: \: \: \: \: \: \implies\sf{\angle A={(39-2)}^{\circ}}$

$\: \: \: \: \: \: \: \: \: \implies\bold{\angle A={37}^{\circ}}$

Required Answer:

$\: \: \: \: \: \leadsto$ ∠A measure 37°