Question

In the figure,line AC is parallel to line DF and line GH is the transversal of angle GBC=55°then find the measures of the remaining angle .angle ABC,angle EBC,angle BEF,angle DEB,angle DEH,angle HEF​

Answer 1

Given :- In the figure,line AC is parallel to line DF and line GH is the transversal of angle GBC=55°then find the measures of the remaining angle .angle ABC,angle EBC,angle BEF,angle DEB,angle DEH,angle HEF ?

Solution :-

from image we have :-

• AC || DF .
• Transversal GH cuts AC at B and DF at E.
• ∠GBC = 55° .

now,

→ ∠ABC = 180° (Ans.) { AC is a straight line.}

and,

→ ∠EBC = 180° - ∠GBC { linear pair .}

→ ∠EBC = 180° - 55°

→ ∠EBC = 125° (Ans.)

Now,

→ ∠CBE + ∠BEF = 180° { interior angles on the same side of the transversal are supplementary. }

→ 125° + ∠BEF = 180°

→ ∠BEF = 180° - 125°

→ ∠BEF = 55° (Ans.)

Now,

→ ∠DEB + ∠BEF = 180° { linear pair .}

→ ∠DEB + 55° = 180°

→ ∠DEB = 180° - 55°

→ ∠DEB = 125° (Ans.)

and,

→ ∠DEH = ∠BEF { vertically opposite angles. }

→ ∠DEH = 55° (Ans.)

Similarly,

→ ∠HEF = ∠DEB { vertically opposite angles. }

→ ∠HEF = 125° (Ans.)

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Answer 2

Answer:

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Step-by-step explanation:

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