Answer:
1. Vertical angles. X = 128º
2. The two angles labeled make up a linear pair & are supplementary, meaning they add up to 180º.
So:
7x + (x+20) = 180
Solve for x:
7x + (x + [20-20]) = 180 - 20
7x + (1)x = 160
8x = 160
X = 20
3. The two angles are complementary, meaning they add up to 90º.
So:
X + 35 = 90
Solve for x:
X + (35-35) = 90 - 35
X = 55
4. the two angles are complementary, and add up to 90º.
So:
4x + 2x = 90
Solve for x:
6x = 90
6x/6 = 90/6
X = 15.
5. Vertical angles, so they are equal in measure.
So:
75 = 4x - 25
Solve for x:
75 + 25 = 4x (-25 + 25)
100 = 4x
100/4 = 4x/4
X = 25.
6. The 3 angles all add up to 180º. they are supplementary.
So:
75 + x + (3x + 5) = 180
Solve for x:
(75 - 75) + x + (3x + 5) = 180 - 75
X + (3x + 5) = 105
X + 3x + (5-5) = 105 - 5
(1) x + 3x = 100
4x = 100
4x/4 = 100
X = 25
7. The 2 angles shown in the picture add up to 180º & are supplementary.
So:
x + (2x - 21) = 180
Solve for x:
X + (2x [-21 + 21]) = 180 - 21
(1)x + 2x = 159
3x = 159
3x/3 = 159/3
X = 53.
Sorry for the late response.
hope this helps & have a great rest of your day!