What is the reason for step 2 in this proof?

given:

angles a and b are supplementary.
the measure of angle a = 45º.

find the measure of angle b. proof:

1. angles a and b are supplementary and angle a = 45º. (reason: given)

2. measure of angle a + measure of angle b = 180º ( reason: ? ? )

3. 45º + measure of angle b = 180º (reason: substitution)

4. measure of angle b = 135º (reason: subtraction property of equality)

a) substitution property of equality
b) definition of supplementary angles
c) transitive property of equality

Angles A and B are said to be supplementary. This piece of information should be used. Supplementary angles are angles whose sum equals 180˚. This would be later used in the further steps to fin the unknown angle B.

Thus, the answer is B) Definition of Supplementary Angles

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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