What Are Remote Interior Angles

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Can the exterior angles of a triangle be acute?

Yes If the interior angle of the triangle is obtuse and then the outside angle will be acute. Conversely, if the interior angle is acute then the outside angle of the triangle volition exist birdbrained.

Detect measure ∠A and ∠C

thousand∠A + m∠B+yard∠C =180°

36 + 10 + (x + 4) = 180

forty + 2x = 180

2x = 140

ten = 70 = m∠A

x + 4 = 74 = g∠B

Exterior Bending of a Triangle

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exterior angle of a triangle with 45 and 90 degree

exterior angle of a triangle with a 45 degree

triangle exterior angle theorem

Exterior Angle Formula

Exterior angles of a triangle

Find the measure of the exterior bending A

Step one. Extend out a line from the side by side side.

Step 2.180-45 =135°

Step 3. The measure of angle a = 135°

Notice the measure of the outside angle D

Pace ane. Plug the given angle measurements into the exterior angle measure out formula

thou∠D= m∠B+m∠C

45 + 90 = 135°

Stride 2. The measure of angle D = 135°

The measure of an outside angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles

The measure of an exterior angle of a triangle is greater than either of the two remote interior angles.

The mensurate of the outside angle is supplementary to the interior bending.

linear pair of angles with a triangle

measure of exterior angle

interior and exterior angles of a triangle illustrated

The Outside Angle is the angle between ane side of a triangle, and a line extended from the side by side side .

What is an outside bending?

triangle with the rmote interior angles highlighted

Remote Interior Angles

The remote interior angles of a triangles are the ii angles that are not adjacent to the exterior bending.The remote interior angles do not share the vertex of the exterior angle.

The measure of the Exterior Angle is equal to the sum measure of the remote interior angles

Hi Welcome to MooMooMath. Today we are going to look at the mensurate of the exterior angle of a triangle. We have a triangle right here and we merely know one bending. Which angles of the triangle are the exterior angles and which are the interior angles? The interior angles are the iii angles on the within of the triangle. To create an outside bending, I will get to the vertex, and I'm going to extend this side out. This creates an exterior angle that is associated with this 45 degree interior angle, and we know lines add upwards to 180. And then these two add up to what nosotros call a linear pair, they are supplementary, then I can find this exterior angle measure out by taking 180 and subtracting 45 so we end upward with 135 degrees. It is an obtuse angle then this angle is 135 degrees. So let's look at the rules for finding outside angles in a triangle. Offset, you have to create the exterior angle by extending 1 side of the triangle. Next, the measure is supplementary to the interior bending. For example, the interior angle is 30, we extend this side out creating an exterior angle, and nosotros find the mensurate of the angle by subtracting 180 -thirty =150. Therefore, we accept a 150 degree exterior angle. Hope this was helpful.