Question

The angle measurements in the diagram are represented by the following expressions.

\qquad \blueD{\angle A=7x + 40^\circ} ∠A=7x+40 ∘

start color #11accd, angle, A, equals, 7, x, plus, 40, degrees, end color #11accd \qquad\greenD{\angle B=3x + 112^\circ} ∠B=3x+112 ∘

start color #1fab54, angle, B, equals, 3, x, plus, 112, degrees, end color #1fab54

Solve for xxx and then find the measure of \blueD{\angle A}∠Astart color #11accd, angle, A, end color #11accd:

\blueD{\angle A} = ∠A=start color #11accd, angle, A, end color #11accd, equals ^\circ ∘

degrees

Answer 1

Answer:

A=166

Step-by-step explanation:

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Answer 2

Answer:

The correct answer is, $x=18^{\circ}$ and $\angle A=\angle B=166^{\circ}$.

Step-by-step explanation:

Given: The angle measurements in the diagram are represented by the following expressions

$&\angle \mathrm{A}=7 \mathrm{x}+40^{\circ}$

$&\angle \mathrm{B}=3 \mathrm{x}+112^{\circ}$

To find: Solve for $x$

and fins $=d$ measure of $\angle A$ and $\angle B$

Step 1

Properties of angles formed by transversal lines with two parallel lines:

• Corresponding angles are congruent.
• Alternate angles are congruent. (Interiors \ Exterior both )
• Interior angles are supplementary. ( adds up to $180^{\circ}$ )

Step 2

$\angle A=\angle B$ Alternate angles

$&7 x+40^{\circ}=3 x+112^{\circ}$

Subtract 40 from both sides

$7 x+40-40=3 x+112-40$

Step 3

Simplify

$7 x=3 x+72$

Subtract $3 x$ from both sides

$7 x-3 x=3 x+72-3 x$

Simplify

$4 x=72$

Divide both sides by 4

$\frac{4 x}{4}=\frac{72}{4}$

Step 4

Simplify

$x=18$

$&\angle \mathrm{A}=7 x+40^{\circ}=7\left(18^{\circ}\right)+40^{\circ}=166^{\circ}$

$&\angle B=3 x+112^{\circ}=3\left(18^{\circ}\right)+112^{\circ}=166^{\circ}$

Therefore, $x=18^{\circ}$ and

$\angle A=\angle B=166^{\circ}$.

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