Question

2-18 72 20=34-To=315)-10=35 5)EXTENSION: a) In right A DEF, m D = 90 and mZF is 12 degrees less than twice mze. Find mZE. b) in AABC, the measure of ZB is 21 less than four times the measure of LA, and the measure of ZC is 1 more than five times the measure of ZA. Find the measure, in degrees, of each angle of ABC.

Answer 1

As given by the question

There are given that in the right triangle DEF, angle D is 90 degrees and angle f is 12 degrees less than angle E.

Now,

The sum of the three measures of a triangle is always 180 degree

So,

`m\angle D+m\angle E+m\angle F=180`

Where angle D is 90 degree

Then,

`\begin{gathered} m\angle D+m\angle E+m\angle F=180 \\ 90+m\angle E+m\angle F=180 \\ m\angle E+m\angle F=90 \end{gathered}`

Also we are given that

`\begin{gathered} F+12=2E \\ F=2E-12 \end{gathered}`

Therefore, substituting for F back into E+F=90

Then,

`\begin{gathered} E+(2E-12)=90 \\ 3E-12=90 \\ 3E=102 \\ E=34 \end{gathered}`

So, angle E is 34 degrees, which is the answer.