b) The exterior angles obtained on producing the base of a triangle on
both ways are 104 degrees and 136 degrees. Find all the angles of the
triangle.
A
136
104
B
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Answer:
Let B and C be the vertex having exterior angles 104
o
and 136
o
respectively.
Ext∠B=104
o
and Ext∠C=136
o
Using theorem "Exterior angle is the sum of interior opposite angles", we get
∠A+∠B=104
o
.......... (1)
∠A+∠C=136
o
.......... (2)
Adding equation (1) and (2)
∠A+∠A+∠B+∠C=240
o
As we know, ∠A+∠B+∠C=180
o
Hence, ∠A=240
o
−180
o
=60
o
From equation (1),
∠B=104
o
−60
o
=44
o
From equation (2),
∠C=136
o
−60
o
=76
o
Hence, angles of the triangle are ∠A=60
o
,∠B=44
o
and ∠C=76
o
.
Step-by-step explanation:
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