L J M K (2x – 15)0 x0 500

1 2 1200 600

1 2

x0 y0 B A C D A common mistake many students make is they think the interior angle x is equal to exterior angle y. These two angles are not equal but they are supplementary.

A C B In addition to its three interior angles, a triangle can have exterior angles formed by one side of the triangle and the extension of an adjacent side. Each exterior angle of a triangle has two remote interior angles that are not adjacent to the exterior angle.

x + 57 = 180 x = 123 570 x0 B A C D The exterior angle of the triangle is supplementary to the adjacent angle that measures 57 degrees. Find the measurement of angle ABD. To solve for x, you can set up an equation x plus 57 equals 180 and solve.

x0 y0 270 520 C A B D 52 + 27 + x = 180 73 + x = 180 x = 107 x + y = 180 y = 73 Find the value of x and y. We can find the value of x by finding the sum of the angle measurements and setting them equal to 180. Once we find the value of x then we can find y by using our knowledge of supplementary angles

52 + 27 + x = 180 and x + y = 180 x0 y0 270 520 C A B D What do you notice about the measure exterior angle measurement and the other two angle measurements in the triangle? If angle ABC and angle ABD are supplementary and angle A, angle B and angle C are supplementary, then the exterior angle must be equal to the sum of the exterior angles.

(2x – 15) + (x – 5) = 148 3x – 20 = 148 3x = 168 x = 56 (2x – 15)0 1480 (2x – 15)0 (x – 5)0 How can we use the ideas of what we just discovered about exterior angles and interior angles to help us solve this problem. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. So we can set up an equation where 2x – 15 plus x – 5 is equal to 148. Then we can solve for x.

L J M K (2x – 15)0 x0 500

1120 320 x0

370 (3x + 47)0 (5x + 62)0 B A C D

(100)0 (2x + 27)0 (2x – 11)0 B A C

(x + 16)0 (5x)0 (3x – 7)0 B A C