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.

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- Apr 23rd 2008, 05:36 PMstellina_91Angle Help Please
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. - Apr 23rd 2008, 10:02 PMSoroban
Hello, stellina_91!

I assume that $\displaystyle EFHD$ is a straight line.

In $\displaystyle \Delta CFD\!:\;\angle EFI$ is an exterior angle.

. . Hence: .$\displaystyle \angle EFI \:=\:\angle C + \angle D \:=\:20^o + 35^o \quad\Rightarrow\quad \angle EFI\:=\:55^o$

In $\displaystyle \Delta AIB\!:\;\angle EIF$ is an exterior angle.

. . Hence: .$\displaystyle \angle EIF \:=\:\angle A + \angle B \:=\:45^o + 30^o\quad\Rightarrow\quad\angle EIF = 75^o$

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

- Apr 24th 2008, 10:25 AMgdbaillargeon