ANSWERS
D) m∠F = 84°
E) z = 15
EXPLANATION
Triangle ABC and triangle FED are similar. This means that they have congruent interior angles, so,
[tex]\begin{gathered} m\angle A=m\angle F \\ m\angle B=m\angle E \\ m\angle C=m\angle D \end{gathered}[/tex]
D) If angle F is congruent to angle A, and we know that the measures of angles B and C are 60° and 36°, knowing that the sum of the measures of the interior angles of any triangle is 180°, we can find the measure of angle F,
[tex]m\angle F=m\angle A=180-60-36=84[/tex]
Hence, the measure of angle F is 84°.
E) As explained above, angle E, whose measure is 4z°, is congruent to angle B, whose measure is 60°, so we have an equation for z,
[tex]4z=60[/tex]
Divide both sides by 4 to solve for z,
[tex]\begin{gathered} \frac{4z}{4}=\frac{60}{4} \\ \\ z=15 \end{gathered}[/tex]
Hence, the value of z is 15.
