Question

find the measure of each marked angle.

x° = □°
(x + 20)° = □°
(180 − 3x)° = □°
(simplify your answers. type integers or fractions.)

Explanation:

Step1: Use triangle angle sum theorem

The sum of the interior angles of a triangle is \(180^\circ\). So we set up the equation: \(x+(x + 20)+(180-3x)=180\).

Step2: Simplify the left - hand side

Combine like terms: \(x+x + 20+180-3x=180\)
\((x + x-3x)+(20 + 180)=180\)
\(-x+200 = 180\)

Step3: Solve for x

Subtract 200 from both sides: \(-x=180 - 200=-20\)
Multiply both sides by - 1: \(x = 20\)

Step4: Find \((x + 20)^\circ\)

Substitute \(x = 20\) into \(x + 20\): \(20+20=40\), so \((x + 20)^\circ=40^\circ\)

Step5: Find \((180-3x)^\circ\)

Substitute \(x = 20\) into \(180-3x\): \(180-3\times20=180 - 60 = 120\), so \((180-3x)^\circ=120^\circ\)

Answer:

\(x^\circ=\boldsymbol{20}^\circ\)
\((x + 20)^\circ=\boldsymbol{40}^\circ\)
\((180-3x)^\circ=\boldsymbol{120}^\circ\)