Question

what is m∠f? m∠f = °

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In \(\triangle DEF\), we have \(\angle F=(x - 13)^{\circ}\), \(\angle E=(x - 33)^{\circ}\), and \(\angle D\) is an inscribed - angle subtended by a semi - circle, so \(\angle D = 90^{\circ}\). Then the equation based on the angle - sum property of a triangle is \((x - 13)+(x - 33)+90 = 180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(x-13+x - 33+90=(x + x)+(-13-33 + 90)=2x+44\). So the equation becomes \(2x+44 = 180\).

Step3: Solve for \(x\)

Subtract 44 from both sides of the equation: \(2x=180 - 44\), so \(2x = 136\). Then divide both sides by 2: \(x=\frac{136}{2}=68\).

Step4: Find the measure of \(\angle F\)

Substitute \(x = 68\) into the expression for \(\angle F\). \(\angle F=(x - 13)^{\circ}\), so \(\angle F=(68 - 13)^{\circ}=55^{\circ}\).

Answer:

55