Question

In the figure given below,

$\angle$1 = $\angle$3 , ​​​​​​​$\angle$2 = ​​​​​​​$\angle$4 and ​​​​​​​$\angle$3 = ​​​​​​​$\angle$4. What is the relation between ​​​​​​​$\angle$1 and $\angle$2?

• A. $\angle$1 = $2$ ​​​​​​​($\angle$2)
• B. $\angle$1 = $\angle$2
• C. $\angle$1 = $\frac{1}{2}$$\angle$2
• D. $\angle$1 = $\angle$2 + 90${}^{\circ }$

Answer 1

The correct option is B $\angle$1 = $\angle$2

Given,
$\angle$2 = $\angle$4 and $\angle$3 = ​​​​​​​$\angle$4.
From Euclid's axioms, we know
"Things that are equal to the same thing are equal to one another."
$\because$ ​​​​​​​$\angle$2 and ​​​​​​​$\angle$3 are equal to the same thing i.e., ​​​​​​​​$\angle$4, ​​​​​​​$\angle$2 = ​​​​​​​$\angle$3.
$\therefore$ ​​​​​​​$\angle$2 = ​​​​​​​$\angle$3

Also, it is given,
​​​​​​​$\angle$1 = ​​​​​​​$\angle$3
$\therefore$ From Euclid's axioms ​​​​​​​$\angle$1 = ​​​​​​​$\angle$2