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In a triangle, if two angles are 45 degrees and 65 degrees, what is the third angle?
60
70
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90
70
Subtract the sum of the two given angles from 180 directly: 180−(45+65)=180−110=70.
Two angles of a triangle are 45 degrees and 65 degrees.
∠A+∠B+∠C=180°
Subtract the sum of the two given angles from 180 directly: 180−(45+65)=180−110=70.
Students often miscalculate the sum of the two angles or subtract from 360 degrees, which is the sum of angles in a quadrilateral, not a triangle.
Identify Angle Sum Property
The sum of all internal angles in any triangle is always 180 degrees.
Sum=180°
Set up Equation
Let the third angle be x. The sum is given by 45°+65°+x=180°.
45°+65°+x=180°
Calculate the Sum of Given Angles
Add the two known angles: 45+65=110.
110°+x=180°
Solve for Third Angle
Subtract 110 from 180 to find x.
x=180°−110°=70°
B is correct because the sum of angles in a triangle is 180 degrees, and 180 - (45 + 65) equals 70.
This concept is foundational for solving problems involving polygons where the sum of interior angles is calculated using the formula (n−2)×180°, where n is the number of sides.
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