Question

Find the value of x
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Answer 1

Answer

To find the value of x in the given figure, we are going to use two concepts such as the 'Straight line angle property' and the 'Angle sum property of quadrilateral'. First, we should find all the interior angles of the given figure.

We can see that, the figure attached in the answer has the markings of angles a, b, c and d. First, we'll find the values of those.

Value of ∠A :

$\sf \dashrightarrow Straight \: line \: angle = {180}^{\circ}$

$\sf \dashrightarrow {50}^{\circ} + \angle{a} = {180}^{\circ}$

$\sf \dashrightarrow \angle{a} = 180 - 50$

$\sf \dashrightarrow \angle{a} = {130}^{\circ}$

Value of ∠B :

$\sf \dashrightarrow Straight \: line \: angle = {180}^{\circ}$

$\sf \dashrightarrow {90}^{\circ} + \angle{b} = {180}^{\circ}$

$\sf \dashrightarrow \angle{b} = 180 - 90$

$\sf \dashrightarrow \angle{b} = {90}^{\circ}$

Value of ∠C :

$\sf \dashrightarrow Straight \: line \: angle = {180}^{\circ}$

$\sf \dashrightarrow {110}^{\circ} + \angle{c} = {180}^{\circ}$

$\sf \dashrightarrow \angle{c} = 180 - 110$

$\sf \dashrightarrow \angle{c} = {70}^{\circ}$

Value of ∠D :

$\sf \dashrightarrow {Angle \: sum \: property}_{(Quadrilateral)} = {360}^{\circ}$

$\sf \dashrightarrow \angle{a} + \angle{b} + \angle{c} + \angle{d} = {360}^{\circ}$

$\sf \dashrightarrow {130}^{\circ} + {90}^{\circ} + {70}^{\circ} + \angle{d} = {360}^{\circ}$

$\sf \dashrightarrow {290}^{\circ} + \angle{d} = {360}^{\circ}$

$\sf \dashrightarrow \angle{d} = 360 - 290$

$\sf \dashrightarrow \angle{d} = {70}^{\circ}$

Now, we can find the value of the angle x.

Value of ∠x :

$\sf \dashrightarrow Straight \: line \: angle = {180}^{\circ}$

$\sf \dashrightarrow {70}^{\circ} + \angle{x} = {180}^{\circ}$

$\sf \dashrightarrow \angle{x} = 180 - 70$

$\sf \dashrightarrow \angle{x} = {110}^{\circ}$

Hence, the value of ∠x is 110°.