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In an isosceles triangle ABC, AB = AC. The exterior angle made at vertex A is 140°. Find the angle opposite to the unequal side of the triangle.
- a)100°
- b)70°
- c)40°
- d)Cannot be determined
Correct answer is option 'C'. Can you explain this answer?
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In an isosceles triangle ABC, AB = AC. The exterior angle made at ver...
Given:
- ABC is an isosceles triangle with AB = AC
- Angle made at vertex A is an exterior angle and it is 140°
To find:
- The angle opposite to the unequal side of the triangle
Solution:
Let's assume that AB = AC = x (because it is given that ABC is an isosceles triangle)
Let's also assume that angle BAC = y (because we want to find the angle opposite to the unequal side)
Now, we know that the sum of angles in a triangle is 180°. So,
Angle BAC + Angle ABC + Angle ACB = 180°
y + (180° - 2y) + (180° - 2y) = 180°
Solving this equation, we get:
y = 40°
Therefore, the angle opposite to the unequal side (which is angle ABC or angle ACB) is:
180° - 2y = 180° - 2(40°) = 100°
Hence, the answer is option C (40°).
- ABC is an isosceles triangle with AB = AC
- Angle made at vertex A is an exterior angle and it is 140°
To find:
- The angle opposite to the unequal side of the triangle
Solution:
Let's assume that AB = AC = x (because it is given that ABC is an isosceles triangle)
Let's also assume that angle BAC = y (because we want to find the angle opposite to the unequal side)
Now, we know that the sum of angles in a triangle is 180°. So,
Angle BAC + Angle ABC + Angle ACB = 180°
y + (180° - 2y) + (180° - 2y) = 180°
Solving this equation, we get:
y = 40°
Therefore, the angle opposite to the unequal side (which is angle ABC or angle ACB) is:
180° - 2y = 180° - 2(40°) = 100°
Hence, the answer is option C (40°).
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Community Answer
In an isosceles triangle ABC, AB = AC. The exterior angle made at ver...
From the figure above, it is clear that sum of 
B and 
C is 140°.
B and C is 140°.Hence, 
A = 180° - 140° = 40°
A = 180° - 140° = 40°Attention CAT Students!
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In an isosceles triangle ABC, AB = AC. The exterior angle made at vertex A is 140°. Find the angle opposite to the unequal side of the triangle.a)100°b)70°c)40°d)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer?
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