Math

QuestionFind xx and the measures of angles (x+20)(x+20) and (4x40)(4x-40).

Studdy Solution

STEP 1

Assumptions1. The two angles are (x+20)(x+20) and (4x40)(4x-40). . The two angles form a straight line, meaning they are supplementary.
3. Supplementary angles add up to180 degrees.

STEP 2

Since the two angles are supplementary, we can set up the following equation(x+20)+(4x40)=180(x+20) + (4x-40) =180

STEP 3

implify the equation by combining like terms.
5x20=1805x -20 =180

STEP 4

To solve for xx, we need to isolate xx on one side of the equation. We can do this by adding20 to both sides of the equation.
x20+20=180+20x -20 +20 =180 +20

STEP 5

implify the equation.
5x=2005x =200

STEP 6

Finally, to solve for xx, divide both sides of the equation by5.
x=2005x = \frac{200}{5}

STEP 7

Calculate the value of xx.
x=2005=40x = \frac{200}{5} =40

STEP 8

Now that we have the value of xx, we can substitute it back into the expressions for the angles to find their measures.The first angle is (x+20)(x+20), so we substitute x=40x =40 into this expression.
Firstangle=(x+20)=(40+20)First\, angle = (x+20) = (40+20)

STEP 9

Calculate the measure of the first angle.
Firstangle=(40+20)=60First\, angle = (40+20) =60^{\circ}

STEP 10

The second angle is (4x40)(4x-40), so we substitute x=40x =40 into this expression.
Secondangle=(4x40)=(44040)Second\, angle = (4x-40) = (4*40-40)

STEP 11

Calculate the measure of the second angle.
Secondangle=(44040)=120Second\, angle = (4*40-40) =120^{\circ}So, the value of the variable xx is40, the measure of the first angle is 6060^{\circ}, and the measure of the second angle is 120120^{\circ}.

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