Question

1. x = m∠e = m∠zgf =

Explanation:

Step1: Apply angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In triangle EFG, we have \((6x + 15)+(10x + 15)+40=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(6x+10x+15 + 15+40=180\), which gives \(16x+70 = 180\).

Step3: Solve for \(x\)

Subtract 70 from both sides: \(16x=180 - 70=110\). Then \(x=\frac{110}{16}=\frac{55}{8}=6.875\).

Step4: Find \(m\angle E\)

Substitute \(x = 6.875\) into the expression for \(m\angle E\). \(m\angle E=6x + 15=6\times6.875+15=41.25+15 = 56.25\).

Step5: Find \(m\angle ZGF\)

Substitute \(x = 6.875\) into the expression for \(m\angle ZGF\). \(m\angle ZGF=10x + 15=10\times6.875+15=68.75+15 = 83.75\).

Answer:

\(x = 6.875\)
\(m\angle E=56.25\)
\(m\angle ZGF = 83.75\)