Angle Help Please

**stellina_91** · April 23rd 2008, 05:36 PM

Find a in the diagram below, giving all reasons.

Could someone please help me with this question. I have no idea where to start!

Thanks.

**Soroban** · April 23rd 2008, 10:02 PM

Hello, stellina_91!

I assume that $EFHD$ is a straight line.

In $\Delta CFD\!:\;\angle EFI$ is an exterior angle.
. . Hence: . $\angle EFI \:=\:\angle C + \angle D \:=\:20^o + 35^o \quad\Rightarrow\quad \angle EFI\:=\:55^o$

In $\Delta AIB\!:\;\angle EIF$ is an exterior angle.
. . Hence: . $\angle EIF \:=\:\angle A + \angle B \:=\:45^o + 30^o\quad\Rightarrow\quad\angle EIF = 75^o$

In $\Delta IEF\!:\;a \:=\:\angle IEF \:=\:180^o - 55^o - 75^o \quad\Rightarrow\quad\boxed{ a\;=\;50^o}$

**gdbaillargeon** · April 24th 2008, 10:25 AM

Originally Posted by stellina_91

Find a in the diagram below, giving all reasons.

Could someone please help me with this question. I have no idea where to start!

Thanks.

The first thing is to realize that in each triangle shown all the angles will add up to 180 degrees. Start there and remember the adjacent opposite angles are equal

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