Prove that-The measure of an exterior angle of a triangle is
equal to sum of its remote interior angles. 2
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4
Answer:
For a given triangle, sum of the three angles =
180
0
∠
1
+
∠
2
+
∠
3
=
180
0
AD is a straight line and CB stands on it.
Therefore, angle 2 and angle 4 are supplementary.
I.e.
∠
2
+
∠
4
=
180
0
Hence
∠
1
+
∠
2
+
∠
3
=
∠
2
+
∠
4
∴
∠
1
+
∠
3
=
∠
4
In other words, exterior angle is equal to sum of the two interior opposite (remote) angles.
Similarly, we can prove the other 5 exterior angles
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