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Difficulty: EasyQuadrilaterals and Polygons

A land surveyor is measuring a four-sided plot of land. They record three of the interior angles as 78∘78^\circ, 104∘104^\circ, and 83∘83^\circ. What is the measure of the fourth interior angle, in degrees?

Answer: 95 degrees

Answer

The fourth interior angle measures 95∘95^\circ.
The correct answer is found by subtracting the sum of the three known angles (265∘265^\circ) from the total interior angle sum of a quadrilateral (360∘360^\circ), which yields 95∘95^\circ.

Step-by-Step Solution

1
Identify the total sum of interior angles for a quadrilateral.
360∘360^\circ
A quadrilateral has 4 sides, and the sum of interior angles is calculated as (n−2)×180∘(n - 2) \times 180^\circ. For n=4n = 4, this is 2×180∘=360∘2 \times 180^\circ = 360^\circ.
2
Calculate the sum of the three given angles.
78∘+104∘+83∘=265∘78^\circ + 104^\circ + 83^\circ = 265^\circ
To find the missing part, we must first determine the combined total of the known angles.
3
Subtract the sum of the given angles from the total quadrilateral angle sum.
360∘−265∘=95∘360^\circ - 265^\circ = 95^\circ
The remaining amount represents the exact measure of the fourth interior angle.

Key Concept

The sum of the interior angles of any convex quadrilateral is always exactly 360∘360^\circ.
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Topics

Quadrilaterals and Polygons

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