Solve Equations with Vertical Angles Quick Check
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
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.
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°
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°.