WARM UP What is the sum of the angle measures of each triangle?

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Presentation transcript:

WARM UP What is the sum of the angle measures of each triangle? Classify each triangle by its angles and side lengths What is the sum of the angle measures of each triangle?

Section 4.2 Angle measures of Triangles

Objective SWBAT find angle measures in triangles.

triangle sum theorem The sum of the measures of the angles of a triangle is 180°. m<A + m <B + m <C = 180° The acute angles of a right triangle are complementary (90°) If m <C =90°, then m<A + m<B = 90°

Finding angle measures of a right triangle Given m<A=43° and m<B=85°, find the m<C m < A + m <B + m <C = 180 ° 43° + 85° + m <C = 180 ° 128° + m <C = 180 ° - 128° - 128 ° m <C = 52 °

Find an angle measure ABC and ABD are right triangles. Suppose m<ABD=35°. Find m < DAB. Find m < BCD m < DAB + m < BCD = 90 ° m < DAB + m <ABC = 90 ° m < DAB + 35° = 90 ° 55° + m < BCD = 90 ° - 35° - 35 ° - 55° - 55 ° m <BCD = 35 ° m < DAB = 55 °

YOU TRY m <A = 65 ° m <B = 75 ° m <C = 50 °

Interior and exterior angles When the three sides of the triangle are extended other angles are formed. The three original angles are the interior angles The angles that are are adjacent to the interior angles are the exterior angles

Exterior angle theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. Symbols: m<1 = m<A + m<B

Find an angle measure Given m < A = 58° and m < C = 72°, find m < 1. m < 1 = m < A + m < C = 58° + 72° = 130°

Find an angle measure Find the value of x. C m < C = m < A + m < B B 136 ° = 94° + x -94° -94° 42° = x

You Try! m<2 = 120° m<3 = 155° m<4 = 113°

Using algebra Find the value of x m< A + m<B + m<C = 180 ° x + 2x + 2x + 15 = 180 ° 5x + 15 = 180 ° - 15 -15 5x = 165 ° __ ___ 5 5 x = 33°

Using algebra Find the value of x m< A + m<C = m<B ___ ___ 6 6 20° = x

You try Find the value of x x = 16