Part Wise Solution:
Find the measure of each angle indicated.
Part 1)
As the measure of three angles in a triangle is 180°. Angle 65° and 57° are given.
Lets suppose the indicated unknown angle is x. So,
65° + 57° + x = 180°
x = 180° - 57° - 65°
x = 58°
So, the indicated unknown angle in part 1) is x = 58°.
Part 2)
Since, it is a right angle triangle. Hence, its one angle would be 90°. Angle 40° is given.
As the measure of three angles in a triangle is 180. Lets suppose the indicated unknown angle is x. So,
90° + 40° + x = 180°
x = 180° - 90° - 40°
x = 50°
So, the indicated unknown angle in part 2) is x = 50°
Part 3)
As the measure of three angles in a triangle is 180. Angle 20° and 130° are given.
Lets suppose the indicated unknown angle is x. So,
20° + 130° + x = 180°
x = 180° - 130° - 20°
x = 30°
So, the indicated unknown angle in part 3) is x = 30°
Part 4)
As the measure of three angles in a triangle is 180°. Angle 85° and 50° are given.
Lets suppose the indicated unknown angle is x. So,
85° + 50° + x = 180°
x = 180° - 85° - 50°
x = 45°
So, the indicated unknown angle in part 4) is x = 45°.
Part 5)
As the angle 102 ° is given. 137 ° is the exterior angle. Let suppose the angle adjacent to exterior angle 137 ° is named "a". Since, an exterior angle angle is supplementary to its adjacent angle. So, 137 ° is supplementary to 43°. So, angle "a" = 43°.
So, angle 102 ° is given and 43° is obtained. Again, as the measure of three angles in a triangle is 180. So, third angle, let suppose named "b", in triangle would be 25°.
As 102 ° + 43° + 35° = 180°
Lets suppose the unknown indicated exterior angle which is to be determined is x.
Since angle b = 35° is adjacent to unknown exterior angle "x". As unknown exterior angle "x" is supplementary to its adjacent angle b = 35°. So, 35° would be supplementary to 145°. Hence, the unknown exterior angle x is 145°.
Part 6)
As the angle 100 ° is given. 35 ° is the outside vertical angle. As outside vertical angle is equal to inside vertical angle. Let suppose the inside vertical angle is named "a". So, angle "a" = 35°.
So, angle 100 ° is given and 35° is obtained. Again, as the measure of three angles in a triangle is 180. So, third angle, let suppose named "b", in triangle would be 45°.
As 100 ° + 35° + 45° = 180°
Lets suppose the unknown indicated exterior angle which is to be determined is x.
Since angle b = 45° is adjacent to unknown exterior angle "x". As unknown exterior angle "x" is supplementary to its adjacent angle b = 45°. So, 45° would be supplementary to 135°. Hence, the unknown exterior angle x is 135°.
Part 7)
Angle 30° and 20° are given. So, the third angle, lets supposed named "a" inside the triangle would be 130° as the measure of three angles in a triangle is 180°.
Lets suppose the unknown indicated outside vertical angle which is to be determined is x.
As the angle "a" = 130° is inside vertical. So, it would be equal to outside vertical which is "x". Hence, x = 130°
Part 8)
As 60° is given interior angle. As we know that the the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. Let Since, 155° is the sum of two non-adjacent interior angles. One interior angle is 60°. Let suppose the other is "a".
So,
155° = 60° + a⇒ a = 95°
As the measure of three angles in a triangle is 180°. So, the third interior angle, let suppose named "b" would be 25°. As 60° + 95° + 25° = 180°.
Lets suppose the unknown indicated exterior angle which is to be determined is x.
As we know that the the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. So, the sides with angle 60° and angle "b" = 25°.
So, x = 60° + 25° = 85°.
Keywords: sum of triangle angles, exterior angle, interior angle
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