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In parallelogram EFGH if GJ=15 find JE.
F
E
H

In parallelogram EFGH if GJ=15 find JE. F E H-example-1
User Brendan Chang
by
3.2k points

1 Answer

16 votes
16 votes

On line EF,


Sum\text{ of angles on a straight line =180}^0

Therefore,

We will have that


\begin{gathered} x^0+119^0=180^0 \\ x^0=180^0-119^0 \\ x^0=61^0 \end{gathered}

Therefore,


\begin{gathered} x=\angle H(\text{Alternate angles are equal)} \\ \text{Hence,} \\ \angle H=61^0 \end{gathered}
\begin{gathered} y=\angle H(corresponding\text{ angles)} \\ \text{therefore,} \\ y=61^0 \end{gathered}

The relationship between y and angle G IS


\begin{gathered} y+\angle G=180^0(Angles\text{ on a straight line)} \\ \angle G+61^0=180^0 \\ \angle G=180^0-61^0 \\ \angle G=119^0 \end{gathered}

In conclusion,


\begin{gathered} y=\angle F((\text{Alternate angles are equal)} \\ \text{therefore,} \\ \angle F=61^0 \end{gathered}

Hence,

Angle G=119°

Angle F=61°

Angle H=61°

In parallelogram EFGH if GJ=15 find JE. F E H-example-1
User Romanb
by
3.6k points