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The angle measurements in the diagram are represented by the following expressions.
\qquad \blueD{\angle A= 5x - 5^\circ}∠A=5x−5
∘
start color #11accd, angle, A, equals, 5, x, minus, 5, degrees, end color #11accd \qquad \greenD{\angle B= 3x + 13^\circ}∠B=3x+13
∘
start color #1fab54, angle, B, equals, 3, x, plus, 13, degrees, end color #1fab54

The Angle Measurements In The Diagram Are Represented By The Following Expressions Qquad BlueDangle A 5x 5circA5x5 Start Color 11accd Angle A Equals 5 X Minus 5 class=

Sagot :

Answer:

x = 9, ∠ B = 40°

Step-by-step explanation:

∠ A and ∠ B are corresponding angles and congruent, so

5x - 5 = 3x + 13 ( subtract 3x from both sides )

2x - 5 = 13 ( add 5 to both sides )

2x = 18 ( divide both sides by 2 )

x = 9

Then

∠ B = 3x + 13 = 3(9) + 13 = 27 + 13 = 40°

The value of the x is 9 and the measure of the angle B is 40 degrees because two parallel lines are cut by a transversal line the adjacent angle made will be equal.

What are vertically opposite angles?

It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.

We have:

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

When the two parallel lines are cut by a transversal line the adjacent angle made will be equal:

Angle A = Angle B

5x - 5 = 3x + 13

Solving the above linear equation:

5x - 3x = 5+13

2x = 18

x = 9

The measure of the angle B = 3x + 13

= 3(9) + 13

= 27 + 13

= 40 degrees

Thus, the value of the x is 9 and the measure of the angle B is 40 degrees because two parallel lines are cut by a transversal line the adjacent angle made will be equal.

Learn more about the vertically opposite angles here:

brainly.com/question/24287162

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