Question

in triangle xyz, angle x = 2x°, angle y=(3x + 8)°, angle z=(3x - 4)°. m∠x = __ °. m∠y = °. m∠z = __ °.

Explanation:

Step1: Apply angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, \(2x+(3x + 8)+(3x-4)=180\).

Step2: Combine like - terms

\((2x+3x + 3x)+(8 - 4)=180\), which simplifies to \(8x+4 = 180\).

Step3: Solve for x

Subtract 4 from both sides: \(8x=180 - 4=176\). Then divide both sides by 8: \(x=\frac{176}{8}=22\).

Step4: Find the measure of each angle

For \(\angle X\): \(m\angle X=2x\), substituting \(x = 22\), we get \(m\angle X=2\times22 = 44^{\circ}\).
For \(\angle Y\): \(m\angle Y=3x + 8\), substituting \(x = 22\), we get \(m\angle Y=3\times22+8=66 + 8=74^{\circ}\).
For \(\angle Z\): \(m\angle Z=3x-4\), substituting \(x = 22\), we get \(m\angle Z=3\times22-4=66-4 = 62^{\circ}\).

Answer:

\(m\angle X = 44^{\circ}\)
\(m\angle Y = 74^{\circ}\)
\(m\angle Z = 62^{\circ}\)