Question

owing questions
(8x - 7)°
(4x + 2)°
77°
x = ______
∠def: ______ °

Explanation:

Step1: Apply triangle - angle sum theorem

The sum of the interior angles of a triangle is 180°. So, \((8x - 7)+(4x + 2)+77=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((8x+4x)+(-7 + 2+77)=180\), which gives \(12x + 72=180\).

Step3: Solve for x

Subtract 72 from both sides: \(12x=180 - 72\), so \(12x=108\). Then divide both sides by 12: \(x=\frac{108}{12}=9\).

Step4: Find the measure of ∠DEF

Substitute \(x = 9\) into the expression for ∠DEF, which is \(4x+2\). So, \(4\times9+2=36 + 2=38\).

Answer:

\(x = 9\)
\(\angle DEF=38^{\circ}\)