A Pentagon and a Square Walk Into a Bar

Geometry Level 2

$ABCDE$ is a regular pentagon. On the outside of $AB$ , we construct a square $ABFG$ . What is the measure (in degrees) of $\angle EAG$ ?

Details and assumptions

The measure of an angle is given as a value from $0^\circ$ to $180^\circ$ .

The answer is 162.

1 solution

Arron Kau Staff
May 13, 2014

From the regular pentagon, we have $\angle EAB = \frac {3 \times 180^\circ }{5} = 108 ^\circ$ . From the square, we have $\angle BAG = 90^\circ$ . Since angles at a point add up to $360^\circ$ , we obtain

$\angle EAG = 360^\circ - 108^\circ - 90^\circ = 162 ^\circ.$

A Pentagon and a Square Walk Into a Bar

The answer is 162.

1 solution

0 pending reports