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The vertex angle of an isosceles triangle measures four times the sum of base angles. Find the measure of base angle.
- a)144°
- b)18°
- c)36°
- d)43°
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The vertex angle of an isosceles triangle measures four times the sum...
In isosceles triangle ABC
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∠B = ∠C = y
⇒ ∠A = 4 × (∠B + ∠C) = 4 × 2 × y = 8y
Sum of all angles in ABC = 180°
⇒ So, ∠A + ∠B +∠C = 180°
⇒ y + y + 8y = 180°
⇒10y = 180°
⇒y = 18°
⇒ ∠B = ∠C = 18°
Hence, the correct option is (B).
Most Upvoted Answer
The vertex angle of an isosceles triangle measures four times the sum...
To solve this problem, let's first understand the given information:
- An isosceles triangle has two equal base angles.
- The vertex angle is the angle opposite the base of the triangle.
Let's assume that the measure of each base angle is x degrees. Since the triangle is isosceles, both base angles are equal. Therefore, each base angle measures x degrees.
According to the given information, the vertex angle measures four times the sum of the base angles. The sum of the base angles is 2x (as both angles are equal). Therefore, the vertex angle measures 4 * 2x = 8x degrees.
Since the sum of the angles in a triangle is always 180 degrees, we can write the equation:
x + x + 8x = 180
Simplifying the equation, we have:
10x = 180
Dividing both sides of the equation by 10, we get:
x = 18
Therefore, each base angle measures 18 degrees. Hence, the correct answer is option B.
- An isosceles triangle has two equal base angles.
- The vertex angle is the angle opposite the base of the triangle.
Let's assume that the measure of each base angle is x degrees. Since the triangle is isosceles, both base angles are equal. Therefore, each base angle measures x degrees.
According to the given information, the vertex angle measures four times the sum of the base angles. The sum of the base angles is 2x (as both angles are equal). Therefore, the vertex angle measures 4 * 2x = 8x degrees.
Since the sum of the angles in a triangle is always 180 degrees, we can write the equation:
x + x + 8x = 180
Simplifying the equation, we have:
10x = 180
Dividing both sides of the equation by 10, we get:
x = 18
Therefore, each base angle measures 18 degrees. Hence, the correct answer is option B.
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The vertex angle of an isosceles triangle measures four times the sum of base angles. Find the measure of base angle.a)144°b)18°c)36°d)43°Correct answer is option 'B'. Can you explain this answer?
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