The sum of the measures of two vertical angles is 300° . Solve for the measure of each angle.(1 point)
Responses
90°
90 degrees
150°
150 degrees
75°
75 degrees
120°
120 degrees
The sum of the measures of two vertical angles is 300° . Solve for the measure of each angle.(1 point)
Responses
90°
90 degrees
150°
150 degrees
75°
75 degrees
120°
None of the given options are correct.
Let's assume one angle to be x°. Since vertical angles are congruent, the other angle will also be x°.
The sum of the measures of two vertical angles is 2x°. According to the given information, 2x° = 300°.
To solve for x, divide both sides of the equation by 2:
2x°/2 = 300°/2
x° = 150°
Therefore, each angle measures 150°.
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
1414
7272
98
We know that vertical angles are congruent, so ∠1 and ∠3 have the same measure.
From the given information, we have:
m∠1 = 4x + 26°
m∠3 = 98°
Setting the two measures equal to each other, we can solve for x:
4x + 26° = 98°
Subtracting 26° from both sides:
4x = 72°
Dividing both sides by 4:
x = 18°
Therefore, 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?(1 point)
Responses
15.3°15.3 degrees
6°6 degrees
53°
53 degrees
29°29 degrees
To find the measure of each angle, we can set the measures of ∠2 and ∠4 equal to each other and solve for x.
Given:
m∠2 = (5x + 23)°
m∠4 = (3x + 35)°
Setting them equal:
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 that we have the value of x, we can substitute it back into either equation to find the measure of each angle.
Using ∠2:
m∠2 = (5x + 23)°
m∠2 = (5*6 + 23)°
m∠2 = (30 + 23)°
m∠2 = 53°
Using ∠4:
m∠4 = (3x + 35)°
m∠4 = (3*6 + 35)°
m∠4 = (18 + 35)°
m∠4 = 53°
Therefore, the measure of each angle is 53°.
Based on the maps, what country is highlighted in red?
(1 point)
Responses
Kenya
Kenya
Mali
Mali
Tanzania
Tanzania
Egypt
Without being able to see the maps you are referring to, I cannot determine which country is highlighted in red. Please provide more information or share the maps for further assistance.
Based on the map, which of the following is the smallest country?
(1 point)
Responses
Algeria
Algeria
Congo
Congo
Gambia
Gambia
Gabon