Question 2

In the given figure, $$FD \parallel BC \parallel AE$$ and $$AC \parallel ED$$

image


The value of $$x$$ is

In $$\triangle ABC$$, $$\angle C = 180^\circ - 51^\circ - 62^\circ = 67^\circ$$. Since $$AE \parallel BC$$, $$\angle EAC = \angle ACB = 67^\circ$$ (alternate angles). AEDF has both pairs of opposite sides parallel, so it is a parallelogram and its adjacent angles are supplementary. Hence $$x = 180^\circ - 67^\circ = 113^\circ$$.

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