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A triangle has one angle that measures 50° and one angle that measures 40°.

What kind of triangle is it?

A.isosceles triangle
B.obtuse triangle
C.right triangle
D.equiangular triangle

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Option A

As we know, a triangle has 180° in total and has three angles.

⇒ Angle 1 + Angle 2 + Angle 3 = 180

We are given the following:

- 1st angle = 50°
- 2nd angle = 40°

Let the 3rd angle be known as "x".

For the triangle to be classified as an isoceles triangle, two angles must be of same measure. Thus, there are two possibilities.

⇒ 50 + 40 + 40 = 180  [Angle 2 = Angle 3]

-------------- Or -------------

⇒ 50 + 40 + 50 = 180  [Angle 1 = Angle 3]

Possibility-1:

- ⇒ 50 + 40 + 40 = 180
- ⇒ 50 + 80 = 180
- ⇒ 130 = 180 (False)

Possibility-2:

- ⇒ 50 + 40 + 50 = 180
- ⇒ 100 + 40 = 180
- ⇒ 140 = 180 (False)

Therefore, the triangle cannot be an isoceles triangle.

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Option B

As we know, a triangle has 180° in total and has three angles.

⇒ Angle 1 + Angle 2 + Angle 3 = 180

We are given the following:

- 1st angle = 50°
- 2nd angle = 40°

Let the 3rd angle be known as "x".

For the triangle to be classified as an obtuse triangle, the third angle must be a measure greater than 90°. Therefore,

- ⇒ 50 + 40 + (x > 90) = 180
- ⇒ 90 + (x > 90) = 180
- ⇒ (x > 90) = 180 - 90
- ⇒ (x > 90) = 90 (False)

This is false because 90 is not greater than 90. Therefore, the triangle is not an obtuse triangle.

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Option C

As we know, a triangle has 180° in total and has three angles.

⇒ Angle 1 + Angle 2 + Angle 3 = 180

We are given the following:

- 1st angle = 50°
- 2nd angle = 40°

Let the 3rd angle be known as "x".

For the triangle to be classified as a right triangle, the third angle must be a measure equivalent to 90°. Therefore,

- ⇒ 50 + 40 + 90 = 180
- ⇒ 90 + 90 = 180
- ⇒ 180 = 180 (True)

Therefore, this triangle is a right triangle.

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Option D

As we know, a triangle has 180° in total and has three angles.

⇒ Angle 1 + Angle 2 + Angle 3 = 180

We are given the following:

- 1st angle = 50°
- 2nd angle = 40°

Let the 3rd angle be known as "x".

For the triangle to be classified as an equiangular triangle, all the angles must be equivalent (60°). Therefore,

- ⇒ 1st angle = 2nd angle = 3rd angle
- ⇒ 50 = 40 = 3rd angle (False, because 50 is not equivalent to 40)

Therefore, this triangle is not an equiangular triangle.

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In conclusion, we can conclude that Option C (Right triangle) is correct.
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Right triangle

Step-by-step explanation:

If the triangle has one angle that measures 50 degrees and another angle that measures 40 degrees, then the last angle must measure 90 degrees because the 3 angles of any triangle add up to 180, so we can set up the following:

180 - (50 + 40) = 90 degrees.

Any triangle that has a 90 degree angle is automatically a right triangle.

Hope this helps!
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