Question

In the figure, $BD\parallel CE$, $AC=BC$, $\angle ABD={20}^0$ and $\angle ECF={70}^0$, Find $\angle GAC$.

• A. ${130}^0$
• B. ${150}^0$
• C. ${70}^0$
• D. ${110}^0$

Answer 1

The correct option is A ${130}^0$

Given, $BD\parallel CE$
$\angle DBC=\angle ECF$ (Corresponding angles)
$\angle DBG+\angle GBC=\angle ECF$
$20+\angle GBC=70$
$\angle GBC={50}^{\circ }$
In $△ABC$,
$BC=AC$
$\angle ABC=\angle CAB={50}^{\circ }$ (Isosceles triangle property)
Now, $\angle CAB+\angle CAG=180$ (Linear pair)
$50+\angle CAG=180$
$\angle CAG={130}^{\circ }$