Question

c) In the given figure, AB//CD, EH//BC, CBAC
= 60° and
LDGH
= 40°.
Find the measures of angles:
AEF
i)
ii)
iii)
ACD
F
AFG
BS​

Answer 1

Answer:

We know that AB || CD and AC is a transversal From the figure we know that ∠BAC and ∠ACD are alternate angles So we get ∠BAC = ∠ACD = 60o So we also get ∠BAC = ∠GCH = 60o From the figure we also know that ∠DHF and ∠CHG are vertically opposite angles So we get ∠DHF = ∠CHG = 50o We know that the sum of all the angles in triangle GCH is 180o. So we can write it as ∠GCH + ∠CHG + ∠CGH = 180o By substituting the values 60o + 50o + ∠CGH = 180o On further calculation ∠CGH = 180o – 60o – 50o By subtraction ∠CGH = 180o – 110o ∠CGH = 70o From the figure we know that ∠CGH and ∠AGH form a linear pair of angles So we get ∠CGH + ∠AGH = 180o By substituting the values 70o + ∠AGH = 180o On further calculation ∠AGH = 180o – 70o By subtraction ∠AGH = 110o Therefore, ∠GCH = 60o and ∠AGH = 110o.

Step-by-step explanation:

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