Question

8 find the m∠yxz. x (3x + 5)° (8x - 14)° b z y (4x)°

Explanation:

Step1: Use the exterior - angle theorem

The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.
So, \(3x + 5+4x=8x - 14\).

Step2: Solve the equation for \(x\)

Combine like terms on the left - hand side: \(7x + 5=8x - 14\).
Subtract \(7x\) from both sides: \(5=x - 14\).
Add \(14\) to both sides: \(x = 19\).

Step3: Find the measure of \(\angle YXZ\)

Substitute \(x = 19\) into the expression for \(\angle YXZ\) (\(3x + 5\)).
\(m\angle YXZ=3x + 5=3\times19+5=57 + 5=62^{\circ}\).

Answer:

\(62^{\circ}\)