The sum of the measure of the angles of a triangle is 1800.

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Presentation transcript:

The sum of the measure of the angles of a triangle is 1800. Find the measure of angle z and x. B 47 + 36 = 83 The sum of the measure of the angles of a triangle is 1800. 470 360 830 970 z 830 x A C D 47 + 36 + z = 180 83 + z = 180 z = 97 ACB and BCD are supplementary 97 + x = 180 x = 83

remote interior angles exterior angle E A B 470 360 970 1440 1440 z 47 + 97 = 144 C ABC and CDE are supplementary 36 + z = 180 z = 144

remote interior angles B 470 360 970 exterior angle 1330 z E C 36 + 97 = 133 CAB and BAE are supplementary 47 + z = 180 z = 133

Exterior Angle Theorem B Exterior Angles x y w A C An exterior angle of a triangle is an angle formed by a side of the triangle and the extension of another side of the triangle. w is an exterior angle of triangle ABC x & y are nonadjacent interior angles often called remote interior angles The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. w = x + y Exterior Angle Theorem

Exterior Angle Theorem Find the value of variable s 130 128.50 Exterior Angle Theorem s0 s0 + 130 = 128.50 s0 = 115.50 Find the value of variable s 50o 130o 80o so 50o Isosceles triangle Converse of the Base angles of an isosceles triangle are congruent.

Exterior Angle Theorem Model Problems = 70 105 = 35 70 F mQTS = mx = 70 alternate interior s 105 = 70 + z Exterior Angle Theorem 35 = z

Model Problems Explain how you find m3 if m5 = 130 and m4 = 70. 5 2 3 1 4 = 130o = 70o m5 is an exterior angle of a triangle. Its measure equals the sum of m3 + m4, the remote interior angles of the triangle. Given that m5 = 1300 and m4 = 700, m3 must be 600, the difference between m5 and m4.

Model Problems C 80o 2x + 30 130o 50o xo 50o xo D A B Isosceles triangle mDAC + mCAB = 180 2x + 30 + x = 180 3x + 30 = 180 3x = 150 x = 50 Base angles of an isosceles triangle are congruent.

Exterior Angle Theorem The measure of an exterior angle of a triangle is 1200. If the measure of one of the remote angles is 200 less than three times the other remote angle, find the measure of the two remote angles. Exterior Angle Theorem 3x - 20 1200 x x = smaller of two remote angles = 35 3x - 20 = larger of two = 85 3x – 20 + x = 120 1200 4x – 20 = 120 4x = 140 x = 35