EXTERIOR ANGLE PROPERTY OF A TRIANGLE

The exterior angle is equal to the sum of the two opposite interior angles.

Find a in the following, giving brief reasons :

Example 1 :

Solution :

The exterior angle is equal to the sum of the two opposite interior angles.

m∠A = 70°, m∠B = a° (interior angles)

m∠D = 125° (exterior angle)

m∠A + m∠B = m∠D

70° + a° = 125°

Subtract 70° from both sides.

a° = 55°

Example 2 :

Solution :

m ∠A = 90°, m∠B = 45° (interior angles)

m∠D = a° (exterior angle)

m∠D = m∠A + m∠B

a° = 90° + 45°

a° = 135°

Example 3 :

Solution :

m ∠A = 101°, m∠B = 45° (interior angles)

m∠D = a° (exterior angle)

m∠D = m∠A + m∠B

a° = 101° + 45°

a =  146°

Example 4 :

Solution :

m ∠A = a°, m∠B = 63° (interior angles)

m∠D = 132° (exterior angle)

m∠A + m∠B = m∠D

a°  + 63° = 132°

Subtract 63° from both sides.

a° = 69°

Example 5 :

Solution :

m ∠A = a°, m∠B = 62° (interior angles)

m∠D = 117° (exterior angle)

m∠A + m∠B = m∠D

a° + 62° = 117°

Subtract 62° from both sides.

a° = 55°

Example 6 :

Solution :

m ∠A = 40°, m∠B = 90° (interior angles)

m∠D = a° (exterior angle)

m∠D = m∠A + m∠B

a° = 40° + 90°

a° = 130°

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