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If the three angles of a quadrilateral are 70°, 85° and 95°, then find the fourth angle.
115°
105°
110°
100°
110°
Use the angle sum property of a quadrilateral: the sum of all four interior angles is always 360°. Subtract the sum of the three given angles from 360° to find the fourth angle.
Three angles of a quadrilateral are 70°, 85°, and 95°
∠A+∠B+∠C+∠D=360°
Use the angle sum property of a quadrilateral: the sum of all four interior angles is always 360°. Subtract the sum of the three given angles from 360° to find the fourth angle.
Students sometimes mistakenly use the triangle angle sum property (180°) instead of the quadrilateral angle sum property (360°).
Step 1: Understand the Property
The sum of all four interior angles in any quadrilateral is always equal to 360°.
∠A+\angle B+\angle C+\angle D=360°
Step 2: Sum the Given Three Angles
Add the three given angles together: 70°+85°+95°=250°.
70°+85°+95°=250°
Step 3: Calculate the Fourth Angle
Subtract the sum of the three angles from the total sum of angles in a quadrilateral (360°).
x=360°−250°=110°
C is correct because the sum of the four angles of a quadrilateral is 360°, and subtracting the sum of the three given angles (70°+85°+95°=250°) from 360° yields 110°.
For an n-sided polygon, the sum of interior angles is given by (n−2)×180°. For a quadrilateral (n=4), this formula gives (4−2)×180°=360°.
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