Question

what is the measure of the smallest angle in the right triangle below? (2x)° (x + 6)° 30° 34° 36° 40°

Explanation:

Step1: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). In a right - triangle, one angle is \(90^{\circ}\). So, \(2x+(x + 6)+90=180\).

Step2: Simplify the equation

Combine like terms: \(2x+x+6 + 90=180\), which gives \(3x+96 = 180\).
Subtract 96 from both sides: \(3x=180 - 96\), so \(3x=84\).
Divide both sides by 3: \(x=\frac{84}{3}=28\).

Step3: Find the measures of the non - right angles

For the angle \((2x)^{\circ}\), substitute \(x = 28\), we get \(2x=2\times28 = 56^{\circ}\).
For the angle \((x + 6)^{\circ}\), substitute \(x = 28\), we get \(x + 6=28+6=34^{\circ}\).

Answer:

\(34^{\circ}\)