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Sum of the Measure of the Angles of a Triangle Sketch– Method 3 m∠ABC + m∠CBD + m∠DBE = 180 ̊ because ∠ABE is a straight angle. ∠ABC ≅∠BCD because they are alternate interior angles. ∠EBD ≅∠CDB because they are alternate interior angles. ∠CBD ≅∠DBC Therefore m∠BCD + m∠CBD + m∠CDB = 180 ̊. 8.02 1 It may be necessary to break the drawing into steps so that students can see and mark the congruent angles. . Using this method also leads to the fact that an exterior angle (∠BDF)is supplementary to the adjacent interior angle (∠CBD) and that the exterior angle is congruent to ∠ABD. Its measure is equal to the sum of the other two (remote/non-adjacent) interior angles. 8.02 2 From above, ∠BDF ≅ ∠ABD and ∠ABC ≅∠BCD. m∠BDF = m∠ABC + m∠CBD Therefore the measure of ∠BDF (an exterior angle) is equal to the sum of the measures of ∠BCD and ∠CBD, the remote interior angles. 8.02 3