Exterior Angle Theorem

Definition: The measure of a triangle’s outside angle is equal to the sum of the measures of its opposite interior angles.

Angle d = Angle a + Angle c
∠d = ∠a + ∠c

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Example:

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Solution: 

Using the Exterior Angle Theorem, we can find the measure of Angle x.

Step 1: The exterior angle theorem tells us that the outside angle of a triangle is equal to the sum of the opposite interior angles.
In this problem, the opposite interior angles are 50 degrees and 60 degrees.

Step 2: Using the given information, we can write the following equation for angle x and solve. The answer will be in degrees.

50 + 60 = x

x = 110°

The measure of ∠x is 110°.

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