Question

Given: Z1 and 24 form a linear pair, m 23+ mZ1 = 1801423-Prove: 23 24StepReason21 and 24 form a linear pairGiven21 and 24 are supplementaryDefinition of Supplementary Angles

Answer 1

SOLUTION

Step 1 :

In this question, we were given that:

$m\text{ }\angle\text{ 1 and }\angle4\text{ form a linear pair, m}\angle3\text{ + m }\angle1\text{ =180}$$We\text{ are supposed to prove that }\angle\text{ 3 }\cong\text{ }\angle\text{ 4 }$

Step 2 :

Using the table. we have that:

$\begin{gathered} a.\angle\text{ 1 and }\angle\text{ 4 form a linear pair} \\ \text{REASON : GIVEN} \end{gathered}$$\begin{gathered} b.m\angle\text{ 3 + m}\angle1=180^0 \\ \text{REASON: GIVEN} \end{gathered}$$\begin{gathered} c.\angle\text{ 1 and }\angle\text{4 are supplementary} \\ \text{REASON: } \\ \text{DEFINITION OF SU}\P PLEMENTRY\text{ ANGLES} \end{gathered}$$\begin{gathered} d.m\text{ }\angle\text{ 2 AND m}\angle3\text{ ARE SU}\P P\text{LEMENTARY} \\ \text{REASON: DEFINITION OF SU}\P PLEMENTARY\text{ ANGLES} \end{gathered}$

$\begin{gathered} e.m\angle\text{ 3 }\cong\text{ m }\angle4 \\ \text{REASON: TRANSITIVE PROPERTY OF EQUALITY} \end{gathered}$