Question

The sum of the measures of the interior angles of a triangle are 180 degrees. in a given triangle, the measure of the second angle is twice the measure of the first. the measure of the third angle is 20 degrees more than the measure of the first angle.

Answer 1

Angle 1 = 40

Angle 2 = 80

Angle 3 = 60

Explanation:

Angle 1 + Angle 2 + Angle 3 = 180

Let's substitute angle 1 with n :

Angle 1 = n

Angle 2 = 2(n)

Angle 2 = 2n

Angle 3 = n + 20

Now substitute the new expressions for each angle back into the equation above :

n + 2n + n + 20 = 180

Let's solve for n :

Collect like terms :

4n + 20 = 180

Subtract 20 from both sides :

4n = 160

Divide both sides by 4 :

n = 40

Substitute the value of n back into the angles :

Angle 1 = n = 40

Angle 2 = 2n = 80

Angle 3 = n+20 = 60

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