Question

I need help with example 4 D and 4E please.Scale factor: 5/3x = 15y = 20

Answer 1

ANSWERS

D) m∠F = 84°

E) z = 15

Step-by-step explanation

Triangle ABC and triangle FED are similar. This means that they have congruent interior angles, so,

`\begin{gathered} m\angle A=m\angle F \\ m\angle B=m\angle E \\ m\angle C=m\angle D \end{gathered}`

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,

`m\angle F=m\angle A=180-60-36=84`

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,

`4z=60`

Divide both sides by 4 to solve for z,

`\begin{gathered} (4z)/(4)=(60)/(4) \\ \\ z=15 \end{gathered}`

Hence, the value of z is 15.