Angles in a Triangle
The sum of the interior angles in a triangle is always 180°
a) We are given two angles of 53° and 68°. The missing angle x must add up to 180° with the sum of 53° + 68° = 121°
Subtract from 180°: x = 180° - 121° = 59°
x = 59°
b) We are given the measure of two angles 46° and 71°. Adding 46°+71°=117°.
Subtract from 180°: x = 180° - 117° = 63°
x = 63°
c) This triangle is isosceles. It can be seen because two of the sides have the same tick mark. This means they are congruent, i.e., they have the same length.
The angles formed by the two congruent sides and the base of an isosceles triangle are congruent, thus:
24 + x + x = 180
Simplifying:
24 + 2x = 180
Subtracting 24:
2x = 180 - 24 = 156
Dividing by 2:
x = 156/2
x = 78°