Respuesta :

Answer:

x = 45°

Step-by-step explanation:

Consecutive angles in a parallelogram are supplementary, thus

lower left angle inside the parallelogram = 180° - 117° = 63°

x and 63 form an interior angle of the pentagon.

The sum of the interior angles of a regular pentagon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 5, thus

sum = 180° × 3 = 540°

The size of the interior angle = 540° ÷ 5 = 108°, hence

x + 63° = 108°  ( subtract 63° from both sides )

x = 45°

PHG

Step-by-step explanation:

First of all

the 117° is the same on the opposite diagonally side of the angle

so 117+117 is 234°

360-234 is 126 (parallelogram is 360°)

126/2 is 63° for the other two angles

find interior of pentagon

pentagon has 5 sides split to 3 triangle

equation: 180*(n-2)

so 3*180 is 540°

540/5 is 108° (divide to find the equal angles on pentagon)

FINALLY

to find X

do 108-63 is 45°

therefore X=45°

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