Question

Question 6
Find the angle measure x in the following figures:

Answer 1

(a) Using angle sum property of a quadrilateral,
${50}^{\circ }+{130}^{\circ }+{120}^{\circ }+x={360}^{\circ }$
$\Rightarrow {300}^{\circ }+x={360}^{\circ }$
$\Rightarrow x=360-300$
$\Rightarrow x={60}^{\circ }$

(b) Using angle sum property of a quadrilateral,
${90}^{\circ }+{60}^{\circ }+{70}^{\circ }+x={360}^{\circ }$
$\Rightarrow {220}^{\circ }+x={360}^{\circ }$
$\Rightarrow x={360}^{\circ }-{220}^{\circ }$
$\Rightarrow x={140}^{\circ }$

(c) First base interior angle = ${180}^{\circ }-{70}^{\circ }={110}^{\circ }$
Second base interior angle = ${180}^{\circ }-{60}^{\circ }={120}^{\circ }$
There are 5 sides, n=5
$\therefore Anglesumofapolygon=(n-2)\times {180}^{\circ }$
$=(5-2)\times {180}^{\circ }\times {180}^{\circ }={540}^{\circ }$
$\therefore {30}^{\circ }+x+{110}^{\circ }+{120}^{\circ }+x={540}^{\circ }$
$\Rightarrow {260}^{\circ }+2x={540}^{\circ }$
$\Rightarrow 2x={540}^{\circ }-{260}^{\circ }$
$\Rightarrow x={140}^{\circ }$

(d) Angle sum of a polygon
$=(n-2)\times {180}^{\circ }$
$=(5-2)\times {180}^{\circ }$
$=3\times {180}^{\circ }$
$={540}^{\circ }$
$\therefore x+x+x+x+x={540}^{\circ }$
$\Rightarrow 5x={540}^{\circ }$
$\Rightarrow x={108}^{\circ }$
Hence, each interior angle is ${108}^{\circ }$.