Mathematics

How many pairs of adjacent angles, in all, can you name in figure?


ANSWER

10


SOLUTION
Let the apparently visible angles be  a, b, c & d.
Each angle has 3 adjacent angles.
The combinations are,
for a$$\longrightarrow $$(a,b),  (a, b+c),  (a, b+c+d) and
for b$$\longrightarrow $$(a,b),  (b,c),  (b, c+d) and
for c$$\longrightarrow $$(b,c),  (c, a+b),  (c,d) and
for d$$\longrightarrow $$(c,d),  (d, b+c),  (d, a+b+c) and
(a+b),  (c+d).
Omitting one of the terms which come  twice we have
(a, b+c),  (a, b+c+d),  (a,b),  (b, c+d),  (b,c)  (c, b+a),  (c,d)  (d, b+c),
(d, a+b+c),  (a+b,  c+d) .
So the total number of  the pairs of adjacent angles=10.
Ans- Option D.

 

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Single Correct Medium Published on 09th 09, 2020
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