Question

the three sides of a triangle are produced as shown

Answer 1

Let ∆ ABC whose side BC is produced to d

Let d be angle ACD

b be angle ACB

a be angle CAB

c be angle ACB

To Prove --- d = a + c

AND Further Sum of all three exterior angles = 360°

Proof ------

SUM OF ANGLES OF A TRIANGLE = 180°

IMPLIES

a + b + c = 180° ------- eq(I)

IN THE FIGURE,

b + d = 180° ( since they form Linear Pair )

b + d = 180° ------- eq (II)

COMBINING eq (I) and eq (II) as they both are equal to 180°

a + b + c = b + d

a + c = b + d - b

a° + c° = d°

In the same way,

Other two exterior angle will be equal to

(a + b) & (b + c)

All exterior angles = a + b + b + c + a + c

All exterior angles = 2a + 2b + 2c

All exterior angles = 2 ( a + b + c )

All exterior angles = 2 × 180°

All exterior angles = 360°

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