Question

find the measure of each marked angle.
x° =
(x + 30)° =
(200 - 3x)° =
(simplify your answers. type integers or fractions.)

Explanation:

Step1: Apply angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, $x+(x + 30)+(200-3x)=180$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $x+x + 30+200-3x=(x+x-3x)+(30 + 200)=-x + 230$. So, the equation becomes $-x+230 = 180$.

Step3: Solve for x

Subtract 230 from both sides: $-x=180 - 230=-50$. Multiply both sides by - 1 to get $x = 50$.

Step4: Find the measure of each angle

For the angle $x^{\circ}$, when $x = 50$, the angle is $50^{\circ}$.
For the angle $(x + 30)^{\circ}$, substitute $x = 50$: $x+30=50 + 30=80^{\circ}$.
For the angle $(200-3x)^{\circ}$, substitute $x = 50$: $200-3x=200-3\times50=200 - 150 = 50^{\circ}$.

Answer:

$x^{\circ}=50^{\circ}$
$(x + 30)^{\circ}=80^{\circ}$
$(200-3x)^{\circ}=50^{\circ}$