Question

find the measure of each marked angle.
$x^{circ}=square^{circ}$
$(x + 30)^{circ}=square^{circ}$
$(180 - 3x)^{circ}=square^{circ}$
(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, \(x+(x + 30)+(180-3x)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(x+x + 30+180-3x=180\).
\((x+x-3x)+(30 + 180)=180\).
\(-x+210 = 180\).

Step3: Solve for x

Subtract 210 from both sides: \(-x=180 - 210\).
\(-x=-30\).
Multiply both sides by - 1: \(x = 30\).

Step4: Find the measure of each angle

For \(x^{\circ}\), when \(x = 30\), \(x^{\circ}=30^{\circ}\).
For \((x + 30)^{\circ}\), substitute \(x = 30\): \((30+30)^{\circ}=60^{\circ}\).
For \((180-3x)^{\circ}\), substitute \(x = 30\): \(180-3\times30=180 - 90=90^{\circ}\).

Answer:

\(x^{\circ}=30^{\circ}\)
\((x + 30)^{\circ}=60^{\circ}\)
\((180-3x)^{\circ}=90^{\circ}\)