Question

Provide the missing statement and reasons for the following proof:

a
Given: mZC + m2D = MZA
Prove: m2B + m2 + m2D = 180°
Statement
Reason
S1. m2c + m2D = MZA
R1. Given
S2. ZB and A form a Linear Pair
R2 Definition of Linear Pair
S3. 2B and 2A are supplementary
R3
S4
R4. Definition of supplementary
S5 m2B + m2 + m2D = 180°
R5

Answer 1

The angle B and angle A forms a linear pair. The linear pair of angles are always supplementary angles. So reason R3 is,

Linear pair are supplementary angles.

The sum of supplementary angles is always equal to 180 degrees. So sum of angle A and angle B is equal to 180 degree. Thus statement S4 is,

`\angle A+\angle B=180`

It is given that angle A is equal to the sum of angle C and angle D. So

`\begin{gathered} \angle A+\angle B=180 \\ \angle B+\angle C+\angle D=180\text{ (}\angle A=\angle C+\angle D\text{)} \end{gathered}`

So reason R5 is,

`m\angle C+m\angle D=m\angle A`

Answer:

R3: Linear pair are always supplementary angles

S4:

`m\angle A+m\angle B=180`

R5:

`m\angle C+m\angle D=m\angle A`