The Exterior Angle Theorem states that the exterior angle of a triangle is equal to the sum of the two opposite interior angles (remote interior angles). This is also known as the Exterior Angle theorem. The sum of all the exterior angles of a triangle is 360°.
However, it is not possible for a triangle to have two acute exterior angles. An acute exterior angle means that its supplement is greater than 90 degrees, which will be one of the interior angles of the triangle. Since the interior angles add up to 180°, an acute angle cannot have two acute exterior angles.
To determine the difference between interior and exterior angles of a triangle, draw a triangle that satisfies the conditions stated and check if the two angles are obtuse exterior angles. If a triangle had two acute exterior angles, it would also have to have two interior obtuse angles, which is impossible.
An acute triangle can never have an acute exterior angle, but it can have two acute angles. The correct statement from the given options is that a triangle can have two acute angles because the sum of two acute angles will always be less than 180∘ because individually, either angle is less than 90∘.
📹 Exterior Angle Theorem For Triangles, Practice Problems – Geometry
This geometry video tutorial provides a basic introduction into the exterior angle theorem for triangles. It explains how to use it …
Why can’t there be a triangle with two right angles?
A triangle is unable to possess two right angles as a consequence of the necessity that the sum of its three interior angles must be 180 degrees.
Can a triangle have 3 exterior angles?
The exterior angle of a triangle is the angle formed between one side and its adjacent extended side. There are three exterior angles in a triangle, and the sum of these angles is always equal to 360°. When any side of a triangle is extended, the angle formed with this side and its adjacent side is called the exterior angle. Each exterior angle forms a linear pair with its corresponding interior angle, which is formed inside the triangle where the sides meet at a vertex. The sum of each interior angle and its corresponding exterior angle is equal to 180°, ensuring that the triangle’s angles are symmetrical and can be viewed as a unit circle.
Can a triangle have 2 obtuse angles?
It is not possible for a triangle to have two obtuse angles, as the sum of the angles in question is 180°. The sum of any two obtuse angles and an acute angle exceeds 180°.
What is the maximum number of possible acute angles in a triangle?
A triangle is defined as a polygon with three acute angles, each with a measure less than 90 degrees. The sum of the angles in a triangle is always 180 degrees, which is necessary for the triangle to have a perfect shape.
How many exterior angles of a triangle can be acute?
It is not possible for a triangle to have two angles with measures of 90 degrees or more, as the sum of the interior angles is 180 degrees. Therefore, at least one angle must have a measure of 90 degrees or more, and two angles must be acute.
Can an acute triangle have two acute angles?
A triangle can have two acute angles, as the sum of the angles in a triangle will always be less than 180°. This is because either angle is less than 90° individually.
Is it possible to have a triangle with two acute exterior angles?
A triangle may be defined as a three-sided figure with two right angles and one obtuse angle, in addition to two acute angles. In an obtuse angle triangle, there is one obtuse angle and two acute angles, with the sum of the interior angles equaling 180°. To illustrate, the angles in question measure 20, 130, and 30 degrees, respectively.
Can you have a triangle with two obtuse exterior angles?
It is not possible to form a triangle with two obtuse angles, as a right angle is defined as measuring exactly 90 degrees, and a triangle is therefore unable to contain two obtuse angles.
Can you draw a triangle with exactly 2 right angles?
It is not possible for a triangle to have two right angles, as the sum of the three angles of a triangle is necessarily less than 180°, which is impossible for a triangle with two right angles.
How many acutes can a triangle have?
A triangle is defined as a polygon with at least two acute angles. An acute triangle is a triangle with three acute angles.
Can 1 acute, 1 right, and 1 obtuse form a triangle?
A triangle may possess a single angle of 90° or more, representing a right or obtuse angle, while the remaining two angles must be acute, resulting in a total angle of 180°.
📹 Angles of Triangle: Sum of Interior Angles and Exterior Angle Theorem by @MathTeacherGon
Angles of Triangle: Sum of Interior Angles and Exterior Angle Theorem by @MathTeacherGon Follow me on my social media …
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