Hexagon

Geometry Level 3

The diagram above shows an hexagon.

What is the size of the angle z in degrees ?


The answer is 124.

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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1 solution

Munem Shahriar
May 28, 2017

Using the formula:

Sum of interior angles = ( n − 2 ) × 180 ° (n - 2) × 180°

with n = 6 (because a hexagon has 6 sides)

⇒ ⇒ The interior angles of a hexagon add to 4 × 180 ° = 720 ° 4 × 180° = 720°

The sum of the given angles = 90 ° + 101 ° + 125 ° + 85 ° + 83 ° = 484 ° = 90° + 101° + 125° + 85° + 83° = 484°

So the remaining interior angle = ( 720 ° − 484 ° ) = 236 ° = (720° - 484°) = 236° .

But the remaining interior angle is not z°. It is ( 360 − z ) ° (360 - z)°

Therefore, 360 − z = 236 360 - z = 236 . ⇒ ⇒ z = 124 ° 124°

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