Question

The angles of a pentagon in degrees are $y^{\circ }$, $(y+{20}^{\circ })$, $(y+{40}^{\circ })-(y+{60}^{\circ })$ and $(y+{80}^{\circ })$. The smallest angle of the pentagon is

• A. ${88}^{\circ }$
• B. ${78}^{\circ }$
• C. ${68}^{\circ }$
• D. ${58}^{\circ }$

Answer 1

Answer: (C)

${68}^{\circ }$

Consider the given angles.

$y^{\circ },(y^{\circ }+{20}^{\circ }),(y^{\circ }+{40}^{\circ }),(y^{\circ }+{60}^{\circ }),(y^{\circ }+{80}^{\circ })$

We know that the sum of all angles of pentagon

$y^{\circ }+(y^{\circ }+{20}^{\circ })+(y^{\circ }+{40}^{\circ })+(y^{\circ }+{60}^{\circ })+(y^{\circ }+{80}^{\circ })={540}^{\circ }$

$5y^{\circ }+{200}^{\circ }={540}^{\circ }$

$5y^{\circ }={340}^{\circ }$

Hence, the smallest angle of the pentagon is ${68}^{\circ }$.