Question

please explain how to do this
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Answer 1

We are just going to use the property of exterior angle. It is a very simple and basic question just to help you build your basic geometry knowledge to simplify complicated figures in higher standards.. which I sometimes suffer in doing so because of disliking geometry in school days *sighs*

Part (i) :

If you observe carefully (no need to observe carefully though xD just had to write for some professional feel :sunglasses: xD)

In ∆ABC,∠ACE is exterior angle.

∠BAC + ∠ABC = ∠ACE....(1)

We have been given that ∠BAC = a,∠ABC =b and ∠ GCD = f,so just substitute these values in their respective places in equation (1)

∠a + ∠b = ∠f

∠a = ∠f - ∠b

We represented the angle ∠a in terms of b and f,so our first part is over after an eternity xD

Part (ii) :

In ∆GCD,∠GDE is exterior angle.

∠GCD + ∠CGD = ∠GDE

Given ∠GCD = f,∠CGD = e and ∠GDE = g.

∠f + ∠e = ∠g

∠e = ∠g - ∠f

Killed another one :drum_roll:

Part (iii) :

∠AGF = ∠CGD = e (vertically opposite angles)

In ∆AGF,∠GFB is exterior angle.

∠AGF + ∠GAF = ∠GFB

∠AGF = e,∠GAF = a and ∠GFB = d, substituting these values,

∠e + ∠a = ∠d

So,we have represented d also in terms of a and e,now let's move to the final section.

Part (iv) :

∠GDC + ∠GDE = 180° (LINEAR PAIR)

∠GDC = 180° - ∠GDE

∠GDC = 180° - g

In ∆GCD,∠GCB is exterior angle.

∠CGD + ∠GDC= ∠GCB

e + 180° - g = c

KDS ho gya xD