Complete the proof of the exterior angle theorem.

given: angle acd is an exterior angle of triangle bcd.

prove: angle b + angle c = angle adc

statements:

1. angle adc is an exterior angle of triangle bcd

2.

3. angle adc and angle bcd form a linear pair

4.

5.

6.

7. angle adc = angle b + angle c

reasons:

1. given

2. triangle sum theorem

3.

4.

5.

6.

7. subtraction property of equality

(i need the blanks filled in)

Answer

Step-by-step explanation:

From the attached diagram below,

< ADC + <D = 180° (sum of linear angle) ------------(1)

<B + <C + <D = 180° (sum of interior angle in a triangle)---------(2)

Since the two equations are equal to 180°, We equate the two equation

i.e

(1) = (2)

< ADC + <D = <B + <C + <D

<D from the left hand side will cancel <D on the right hand side

We are now left with

<ADC = <B + <C

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step-by-step explanation:

step-by-step explanation:

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