How do we solve it?
- Empire539Lv 76 years agoFavorite Answer
The sum of the interior angles of any triangle will be 180°. Looking at ∆ACE, we see that we already have two angles. To find the third angle (∠AEC), we know that:
3a + a + m∠AEC = 180
⇒ m∠AEC = 180 − 4a
Since line CE intersects line AD, we also know that ∠AEC is a supplementary angle to ∠CED. So:
m∠CED = 180 − m∠AEC
= 180 − (180 − 4a)
We also know that m∠DFE is opposite to the 60° angle, and they therefore have the same measure.
Now that we have m∠CED (which will be the same as m∠FED) and m∠DFE, and we know that the sum of interior triangles is 180, we can find the missing value of a:
m∠DFE + m∠FED + m∠DEF = 180
⇒ 60 + 4a + 2a = 180
⇒ 60 + 6a = 180
⇒ 6a = 120
⇒ a = 20°
You can check your work by plugging a = 20 into the appropriate angles and seeing if they all add up to 180° as expected.