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?
Responses 98
98
14
18
72
If ∠1 and ∠3 are a vertical pair, that means they are congruent. So we set the measure of ∠1 equal to the measure of ∠3:
m∠1 = m∠3
4x + 26 = 98
Subtract 26 from both sides:
4x = 72
Divide both sides by 4:
x = 18.
The value of x is 18.
For two vertical angles with measures m∠2 = (5x + 23)° and m∠4 = (3x + 35)°, what is the measure of each angle?
Responses
15.3°
53°
6°
29°
Given that two angles are vertical angles, they have equal measures.
So we set up an equation: m∠2 = m∠4
Thus, (5x + 23)° = (3x + 35)°
Now we solve for x:
5x + 23 = 3x + 35
Subtract 3x from both sides: 2x + 23 = 35
Subtract 23 from both sides: 2x = 12
Divide both sides by 2: x = 6
Now substitute the value of x into either equation to find the measure of the angles:
m∠2 = (5x + 23)° = (5 * 6 + 23)° = 53°
m∠4 = (3x + 35)° = (3 * 6 + 35)° = 53°
Therefore, the measure of each angle is 53°.
There are two complementary angles, ∠5 and ∠6. If m∠5 = 39°, what equation can you write to solve for m∠6?
Responses
m∠6 = 39°
m∠6 + 39° = 180°
m∠6 + 39° = 90°
m∠6 = 180° − 39°
If two angles are complementary, that means the sum of their measures is equal to 90 degrees.
So, we can write the equation: m∠5 + m∠6 = 90°
Substituting the given value: 39° + m∠6 = 90°
To solve for m∠6, we can subtract 39° from both sides: m∠6 = 90° - 39°
Simplifying gives us: m∠6 = 51°
So the correct equation to solve for m∠6 is: m∠6 = 51°