Question
Find the unknown marked angles in the given figure:
✓
Answer
We know that in a triangle if one side of it is produced, then
Exterior angle = sum of its interior opposite angles.
In fig., 125° = a + c .......(i)
and 140° = a + b ............(ii)
Adding, we get
a + c + a + b = 125° + 140°
⇒ a + a + b + c = 265°
But a + b + c = 180° ........(sum of angles of a triangle)
∴ a + 180° = 265°
⇒ a = 265° − 180° = 85°
But a + b = 140°
⇒ 85° + b = 140°
⇒ b = 140°− 85° = 55°
and a + c = 125°
⇒ 85° + c = 125°
⇒ c = 125° − 85° = 40°
Hence a = 85°, b = 55° and c = 40°
Exterior angle = sum of its interior opposite angles.
In fig., 125° = a + c .......(i)
and 140° = a + b ............(ii)
Adding, we get
a + c + a + b = 125° + 140°
⇒ a + a + b + c = 265°
But a + b + c = 180° ........(sum of angles of a triangle)
∴ a + 180° = 265°
⇒ a = 265° − 180° = 85°
But a + b = 140°
⇒ 85° + b = 140°
⇒ b = 140°− 85° = 55°
and a + c = 125°
⇒ 85° + c = 125°
⇒ c = 125° − 85° = 40°
Hence a = 85°, b = 55° and c = 40°
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