Question

In the given figure, AB||CD and EF is a transversal . If angle AEF = 65 ° angle DFG = 30 °, angle EGF = 90° and angle GEF = x, find the value of x.
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Answer 1

Answer:

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Step-by-step explanation:

We know that AB∥CD and EF is a transversal

From the figure we know that ∠AEF and ∠EFD are alternate angles

So we get

So we get∠AEF=∠EFG+∠DFG

So we get∠AEF=∠EFG+∠DFGBy substituting the values

So we get∠AEF=∠EFG+∠DFGBy substituting the values65∘=∠EFG+30∘

So we get∠AEF=∠EFG+∠DFGBy substituting the values65∘=∠EFG+30∘On further calculation

So we get∠AEF=∠EFG+∠DFGBy substituting the values65∘=∠EFG+30∘On further calculation∠EFG=65∘−30∘

So we get∠AEF=∠EFG+∠DFGBy substituting the values65∘=∠EFG+30∘On further calculation∠EFG=65∘−30∘By subtraction

So we get∠AEF=∠EFG+∠DFGBy substituting the values65∘=∠EFG+30∘On further calculation∠EFG=65∘−30∘By subtraction∠EFG=35∘

We know that the sum of all the angles in triangle GEF is 180∘.

We know that the sum of all the angles in triangle GEF is 180∘.∠GEF+∠EGF+∠EFG=180∘

We know that the sum of all the angles in triangle GEF is 180∘.∠GEF+∠EGF+∠EFG=180∘By substituting the values we get

We know that the sum of all the angles in triangle GEF is 180∘.∠GEF+∠EGF+∠EFG=180∘By substituting the values we getx+90∘+35∘=180∘

We know that the sum of all the angles in triangle GEF is 180∘.∠GEF+∠EGF+∠EFG=180∘By substituting the values we getx+90∘+35∘=180∘On further calculation

We know that the sum of all the angles in triangle GEF is 180∘.∠GEF+∠EGF+∠EFG=180∘By substituting the values we getx+90∘+35∘=180∘On further calculationx=180∘−90∘−35∘

We know that the sum of all the angles in triangle GEF is 180∘.∠GEF+∠EGF+∠EFG=180∘By substituting the values we getx+90∘+35∘=180∘On further calculationx=180∘−90∘−35∘By subtraction

We know that the sum of all the angles in triangle GEF is 180∘.∠GEF+∠EGF+∠EFG=180∘By substituting the values we getx+90∘+35∘=180∘On further calculationx=180∘−90∘−35∘By subtractionx=55∘

We know that the sum of all the angles in triangle GEF is 180∘.∠GEF+∠EGF+∠EFG=180∘By substituting the values we getx+90∘+35∘=180∘On further calculationx=180∘−90∘−35∘By subtractionx=55∘Therefore, the value of x is 55∘.

Answer 2

Answer:

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