Remote, Exterior and Interior Angles of A Triangle

The Exterior, Interior and Remote Interior Angles

An exterior angle of a triangle, or any polygon, is formed by extending one of the sides of the triangle (or polygon).

In a triangle, each exterior angle has two remote interior angles (see picture below). The remote interior angles are just the two angles that are inside the triangle and opposite from the exterior angle.

Click the purple button below to create an exterior angle.

The exterior angle is supplemental to the adjoining interior angle. Notice: ABC =46° and the exterior angle is 134°.

Formula for Remote Interior Angles and Exterior Angles

As the picture below shows, an exterior angle (A) equals the sum of the remote interior angles.

To rephrase it, the angle 'outside the triangle' (exterior angle A) equals D + C (the sum of the remote interior angles).

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Interactive Demonstration of Remote and Exterior Angles of a Triangle

The interactive program below allows you to drag the points of the triangle around. Notice that the sum of the remote interior angles (C and D) equal the measure of exterior angle A.

Use the formulas described on this page to calcualte the values of x (a remote interior angle) and of Y.

Answer

Since X and J are remote interior angles in relation to the 120° angle, you can use the formula.
120 = 45 + x
120- 45 = x
75° = x.
Now, since the sum of all interior angles of a triangle is 180°. You can solve for Y 75 + 45 + y = 180
120 + Y = 180
Y = 60