Alana is working on creating a scale
1 answer:
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Answer:
x = 100°
Step-by-step explanation:
As the given shape is a regular polygon, the triangles created by extending the sides are <u>isosceles triangles</u>.
To calculate the base angles of the isosceles triangle, find the interior angle of the regular polygon:
Therefore:
As angles on a straight line sum to 180°, the <u>base angle</u> of the isosceles triangle is:
= 180° - interior angle
= 180° - 140°
= 40°
Interior angles of a triangle sum to 180°.
⇒ 2 base angles + x = 180°
⇒ 2 × 40° + x = 180°
⇒ 80° + x = 180°
⇒ x = 180° - 80°
⇒ x = 100°
