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Zorluk: KolayPolygon Angles and Properties

A convex pentagon has four interior angles that measure 80∘80^\circ, 110∘110^\circ, 120∘120^\circ, and 130∘130^\circ. What is the degree measure of the fifth interior angle?

Cevap: 100 degrees

Cevap

The degree measure of the fifth interior angle is 100∘100^\circ.
The sum of the interior angles of a pentagon (n=5n = 5) is (5−2)×180∘=540∘(5 - 2) \times 180^\circ = 540^\circ. The sum of the four given angles is 80∘+110∘+120∘+130∘=440∘80^\circ + 110^\circ + 120^\circ + 130^\circ = 440^\circ. The measure of the fifth angle is the difference between these two values: 540∘−440∘=100∘540^\circ - 440^\circ = 100^\circ.

Adım Adım Çözüm

1
Find the sum of the interior angles of a convex pentagon.
The sum of the interior angles is 540∘540^\circ.
The sum of the interior angles of any nn-sided convex polygon is calculated using the formula (n−2)×180∘(n - 2) \times 180^\circ. For a pentagon, n=5n = 5, which gives (5−2)×180∘=3×180∘=540∘(5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ.
2
Sum the measures of the four given interior angles.
The sum of the four given angles is 440∘440^\circ.
Adding the given measures: 80∘+110∘+120∘+130∘=440∘80^\circ + 110^\circ + 120^\circ + 130^\circ = 440^\circ.
3
Subtract the sum of the four given angles from the total sum of the interior angles.
The measure of the fifth interior angle is 100∘100^\circ.
Subtracting the sum of the known angles from the total pentagon interior angle sum yields 540∘−440∘=100∘540^\circ - 440^\circ = 100^\circ.

Anahtar Kavram

The sum of the interior angles of an nn-sided convex polygon is (n−2)×180∘(n-2) \times 180^\circ.
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Polygon Angles and Properties

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