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Given the diagram below, find the measure of each missing angle.

Type only the number in the blank.
m/1=
11
m22:
m23=
mZ4=
m25
degrees
degrees
degrees
degrees
degrees

Given the diagram below, find the measure of each missing angle. Type only the number-example-1
User Parhum
by
8.1k points

1 Answer

5 votes

Answer:

see explanation

Explanation:

∠ 1 and 130° are a linear pair and sum to 180° , then

∠ 1 + 130° = 180° ( subtract 130° from both sides )

∠ 1 = 50°

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the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

130° is an exterior angle of the triangle on the left , then

∠ 2 + 90° = 130° ( subtract 90° from both sides )

∠ 2 = 40°

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∠ 2 and ∠ 3 are a linear pair and sum to 180° , then

∠ 2 + ∠ 3 = 180° , that is

40° + ∠ 3 = 180° ( subtract 40° from both sides )

∠ 3 = 140°

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∠ 2 and angle inside triangle on right are vertically opposite angles and are congruent (equal )

the triangle on the right has 2 congruent legs and is isosceles with base angles being congruent , then

∠ 5 = 40° ( equal to the vertically opposite angle in the triangle )

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the sum of the 3 angles in a triangle = 180° , then

∠ 4 + ∠ 5 + 40° = 180° , so

∠ 4 + 40° + 40° = 180°

∠ 4 + 80° = 180° ( subtract 80° from both sides )

∠ 4 = 100°

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in summary

∠ 1 = 50° , ∠ 2 = 40° , ∠ 3 = 140° , ∠ 4 = 100° , ∠ 5 = 40°

User Arnis Juraga
by
8.5k points