# Thread: Help needed with Circles ( Properties-Based Questions )

1. ## Help needed with Circles ( Properties-Based Questions )

Greetings to Forum Members, Im kinda stucked in this question so i guess i need some help...

The Informations :

In the diagram, ABE, ADF, BCF and DCE are straight lines. <AED = 30degrees and <AFB = 34degrees. Find <x.

The attempt at a solution :
Since they are Straight Lines, < EBC = 90degrees and thus, < BCE = 60 degrees.
Since <BCE = 60 degrees, <DCF = 60degrees ( vertically opp. angles )
Since <DCF = 60degrees, < CDF = 180 - 34 - 60 = 86 degrees. ( sum of angles in triangle )
Since < CDF = 86 degrees , < ADB = 180 - 86 = 94 degrees.
Therefore, < x = 180 - 94 = 86 degrees ( angles in the opposite segment )

The Problem :
I counter-checked against the answer and i was wrong. Or rather, i do not have enough clues to solve this question. Can someone please ' enlighten ' me ?? Thanks

P/S : Sorry for the inconvenience for having to view my solutions and the question separately as i have no idea on how to have the image shown together with the post.

2. Originally Posted by tgpnlyt7095

Greetings to Forum Members, Im kinda stucked in this question so i guess i need some help...

The Informations :

In the diagram, ABE, ADF, BCF and DCE are straight lines. <AED = 30degrees and <AFB = 34degrees. Find <x.

The attempt at a solution :
Since they are Straight Lines, < EBC = 90degrees and thus, < BCE = 60 degrees.
Since <BCE = 60 degrees, <DCF = 60degrees ( vertically opp. angles )
Since <DCF = 60degrees, < CDF = 180 - 34 - 60 = 86 degrees. ( sum of angles in triangle )
Since < CDF = 86 degrees , < ADB = 180 - 86 = 94 degrees.
Therefore, < x = 180 - 94 = 86 degrees ( angles in the opposite segment )

The Problem :
I counter-checked against the answer and i was wrong. Or rather, i do not have enough clues to solve this question. Can someone please ' enlighten ' me ?? Thanks

P/S : Sorry for the inconvenience for having to view my solutions and the question separately as i have no idea on how to have the image shown together with the post.
Hi tgpnlyt7095,

Quick question....how did you determine that angle EBC = 90 degrees? The fact that they are straight lines has no bearing on what angle is formed when they cross. Did you leave out some important GIVEN information? Is line DF tangent to the circle at C or D?

And lines are not symbolized using 3 letters....just 2.

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### in the figure ,ABE,DCE,BCF,ADF are straight lines .E=50,F=56,find angle A

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