Question

Using the information from the given figure find x.

• A. ${60}^{\circ }$
• B. ${30}^{\circ }$
• C. ${50}^{\circ }$
• D. ${40}^{\circ }$

Answer 1

The correct option is D

${40}^{\circ }$

Sum of all angles of a quadrilateral $={360}^{\circ }$.

$\Rightarrow 70+a=180\left(Linearpair\right)$

$\Rightarrow a=180-70$

$\Rightarrow a={110}^{\circ }$

$a+{80}^{\circ }+{56}^{\circ }+(3x-6{)}^{\circ }={360}^{\circ }(Anglesumporpertyofquadrilateral.)$

$\Rightarrow {110}^{\circ }+{80}^{\circ }+{56}^{\circ }+(3x-6{)}^{\circ }={360}^{\circ }$

$\Rightarrow {246}^{\circ }+3x-6^{\circ }={360}^{\circ }$

$\Rightarrow {240}^{\circ }+3x={360}^{\circ }$

$\Rightarrow 3x={360}^{\circ }-{240}^{\circ }={120}^{\circ }$

$\Rightarrow x={40}^{\circ }$