Solve Equations with Vertical Angles Quick Check

Question

4 of 54 of 5 Items
Question
In a geometric figure two intersecting lines creating four angles. If ∠1 and ∠3 are a vertical pair, m∠1=(4x+26)° , and m∠3=98° , what is the value of x ?(1 point)
Responses

18
18

7272

1414

98

Answer 1

We know that vertical angles are congruent, meaning they have the same measure.

Since ∠1 and ∠3 are a vertical pair, we can set up the equation:

4x + 26 = 98

Subtract 26 from both sides to isolate the term with x:

4x = 72

Divide both sides by 4 to solve for x:

x = 18

Therefore, the value of x is 18.

Answer 2

Solve Equations with Vertical Angles Quick Check
5 of 55 of 5 Items
Question
For two vertical angles with measures m∠2=(5x+23)° and m∠4=(3x+35)°, what is the measure of each angle?(1 point)
Responses

15.3°15.3 degrees

53°
53 degrees

6°6 degrees

29°

Answer 3

Since ∠2 and ∠4 are vertical angles, they have the same measure.

Setting up the equation:

5x + 23 = 3x + 35

Subtracting 3x from both sides:

2x + 23 = 35

Subtracting 23 from both sides:

2x = 12

Dividing both sides by 2:

x = 6

Now substituting the value of x back into the expressions for ∠2 and ∠4:

∠2 = 5(6) + 23 = 30 + 23 = 53°

∠4 = 3(6) + 35 = 18 + 35 = 53°

Therefore, the measure of each angle is 53°.