Question

In each case; given below, find the value of x in terms of a, b and c.

• A. $x={180}^{\circ }-a-b+c$
• B. $x={180}^{\circ }+b+a+c$
• C. $x={180}^{\circ }+b-a-c$
• D. $x={180}^{\circ }+a+b-c$

Answer 1

The correct option is D $x={180}^{\circ }+a+b-c$

From the figure,
$c=\angle ECD+\angle EDC$ (Exterior angle property)
$c=\angle ECD+b$ ...(I)
In $△ABC$,
$\angle ECD=\angle CAB+\angle CBA$ (Exterior angle property)
$\angle ECD=a+\angle CBA$ ($\angle CBA=180-x$ (Linear pair))
$\angle ECD=a+180-x$
Put value in I,
$c=a+180-x+b$
$x=180+a+b-c$