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If one angle of a triangle is equal to the sum of the other two angles, then the triangle is :
- a)an isosceles triangle
- b)a right triangle
- c)an equilateral triangle
- d)an obtuse angled triangle
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If one angle of a triangle is equal to the sum of the other two angles...
Let "a" be the measure of the angle A;
Let "b" be the measure of the angle B;
Let "c" be the measure of the angle C.
Then
a + b + c = 180, (1)
a + b = c. (2) (given).
Add the equation (1) and (2). You will get
2(a+b) + c = 180 + c.
Simplify:
2(a+b) = 180 ---> a + b = 180/2=90
Most Upvoted Answer
If one angle of a triangle is equal to the sum of the other two angles...
Explanation:
To prove that if one angle of a triangle is equal to the sum of the other two angles, then the triangle is a right triangle, we need to use the properties of the angles in a triangle.
Properties of angles in a triangle:
1. The sum of the angles in a triangle is always 180 degrees.
2. In a right triangle, one angle is equal to 90 degrees.
Proof:
Let's assume that one angle of the triangle is x degrees, and the other two angles are y and z degrees.
According to the given condition, we have the equation: x = y + z.
Since the sum of the angles in a triangle is 180 degrees, we can write another equation: x + y + z = 180.
Substituting the value of x from the first equation into the second equation, we get: y + z + y + z = 180.
Simplifying the equation, we have: 2y + 2z = 180.
Dividing both sides of the equation by 2, we get: y + z = 90.
This equation shows that the sum of the other two angles is 90 degrees. According to the properties of angles in a triangle, if the sum of two angles is 90 degrees, then the triangle is a right triangle.
Therefore, the correct answer is option 'B' - a right triangle.
To prove that if one angle of a triangle is equal to the sum of the other two angles, then the triangle is a right triangle, we need to use the properties of the angles in a triangle.
Properties of angles in a triangle:
1. The sum of the angles in a triangle is always 180 degrees.
2. In a right triangle, one angle is equal to 90 degrees.
Proof:
Let's assume that one angle of the triangle is x degrees, and the other two angles are y and z degrees.
According to the given condition, we have the equation: x = y + z.
Since the sum of the angles in a triangle is 180 degrees, we can write another equation: x + y + z = 180.
Substituting the value of x from the first equation into the second equation, we get: y + z + y + z = 180.
Simplifying the equation, we have: 2y + 2z = 180.
Dividing both sides of the equation by 2, we get: y + z = 90.
This equation shows that the sum of the other two angles is 90 degrees. According to the properties of angles in a triangle, if the sum of two angles is 90 degrees, then the triangle is a right triangle.
Therefore, the correct answer is option 'B' - a right triangle.
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