Angle Sum Theory And Triangle Classification

Explanation
The triangle is classified as isosceles because it has two equal sides. It is also classified as right because it has a right angle.

Explanation
Based on the given options, the answer "Obtuse Scalene" is the correct classification for the triangle. An obtuse triangle is a triangle that has one angle greater than 90 degrees. A scalene triangle is a triangle that has three unequal sides. Therefore, if a triangle has one angle greater than 90 degrees and three unequal sides, it can be classified as an obtuse scalene triangle.

Explanation
The missing angle can be found by subtracting the sum of the given angles (40, 110, 80) from 180 degrees. This is because the sum of angles in a triangle is always 180 degrees. Therefore, the missing angle is 180 - (40 + 110 + 80) = 70 degrees.

Explanation
The given answer, "Acute Isosceles," suggests that the triangle in question is both acute and isosceles. An acute triangle is a triangle in which all three angles are less than 90 degrees. An isosceles triangle is a triangle that has two sides of equal length. Therefore, an acute isosceles triangle would have two sides of equal length and all three angles less than 90 degrees.

Explanation
The given triangle has angle measurements of 62 and 57 degrees. Since the sum of the angles in a triangle is always 180 degrees, the third angle can be calculated as 180 - (62 + 57) = 61 degrees.

To classify the triangle by its sides, we need to determine if all sides are equal (equilateral), if two sides are equal (isosceles), or if no sides are equal (scalene). Since no information about the sides is given, we can conclude that the triangle is scalene.

To classify the triangle by its angles, we need to determine if all angles are less than 90 degrees (acute), if one angle is equal to 90 degrees (right), or if one angle is greater than 90 degrees (obtuse). Since all angles in the given triangle are less than 90 degrees, we can conclude that the triangle is acute.

Therefore, the correct classification for the given triangle is "Acute Scalene".

Explanation
The triangle has two angles measuring 120 and 52 degrees, which means that the sum of the angles is greater than 180 degrees, making it an obtuse triangle. Additionally, the triangle has sides of different lengths, making it a scalene triangle. Therefore, the correct classification for this triangle is "Obtuse Scalene."

Explanation
In a triangle, the sum of all three angle measurements is always 180 degrees. To find the missing angle measurement, subtract the sum of the given angles (58 + 73 = 131) from 180. Therefore, the missing angle measurement is 49 degrees.

Explanation
The triangle in the question has one angle that is greater than 90 degrees, making it an obtuse triangle. Additionally, the triangle has two sides that are equal in length, making it an isosceles triangle. Therefore, the classifications that fit the triangle are obtuse and isosceles.

Explanation
The value of x is 30 because it is the last number listed in the given sequence.

Explanation
In order to be classified as an isosceles, it must have AT LEAST 2 congruent sides. An equilateral triangle has 3 congruent sides.