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Problem 1 :
The measure of an angle is 41°. What is the measure of a complementary angle ?
Problem 2 :
The measure of an angle is 62°. What is the measure of a complementary angle ?
Problem 3 :
The measure of an angle is 108°. What is the measure of a supplementary angle ?
Problem 4 :
The measure of an angle is 89°. What is the measure of a supplementary angle ?
Problem 5 :
Two angles are complementary. If one of the angles is double the other angle, find the two angles.
Problem 6 :
Two angles are complementary. If one angle is two times the sum of other angle and 3, find the two angles.
Problem 7 :
Find the value of x :
Problem 8 :
Find the value of x :
Problem 9 :
Find the value of x :
Problem 10 :
Find the value of x :
Problem 1 :
The measure of an angle is 41°. What is the measure of a complementary angle ?
Solution :
Let x be the measure of the required complementary angle.
Because x and 41° are complementary angles,
x + 41° = 90°
Subtract 41° from each side.
x = 49°
So, the measure of the complementary angle is 49°.
Problem 2 :
The measure of an angle is 62°. What is the measure of a complementary angle ?
Solution :
Let x be the measure of the required complementary angle.
Because x and 62° are complementary angles,
x + 62° = 90°
Subtract 62° from each side.
x = 28°
So, the measure of the complementary angle is 28°.
Problem 3 :
The measure of an angle is 108°. What is the measure of a supplementary angle ?
Solution :
Let x be the measure of the required supplementary angle.
Because x and 108° are supplementary angles,
x + 108° = 180°
Subtract 108° from each side.
x = 72°
So, the measure of the supplementary angle is 72°.
Problem 4 :
The measure of an angle is 89°. What is the measure of a supplementary angle ?
Solution :
Let x be the measure of the required supplementary angle.
Because x and 41° are supplementary angles,
x + 89° = 180°
Subtract 89° from each side.
x = 91°
So, the measure of the supplementary angle is 91°.
Problem 5 :
Two angles are complementary. If one of the angles is double the other angle, find the two angles.
Solution :
Let x be one of the angles.
Then the other angle is 2x.
Because x and 2x are complementary angles, we have
x + 2x = 90°
3x = 90
Divide each side by 3.
x = 30
And,
2x = 2(30) = 60
So, the two angles are 30° and 60°.
Problem 6 :
Two angles are complementary. If one angle is two times the sum of other angle and 3, find the two angles.
Solution :
Let x and y be the two angles which are complementary.
So, we have
x + y = 90° -----> (1)
Given : One angle is two times the sum of other angle and 3.
Then,
x = 2(y + 3)
x = 2y + 6 ----->(2)
Now, substitute (2y + 6) for x in (1).
(1)-----> 2y + 6 + y = 90
3y + 6 = 90
Subtract 6 from each side.
3y = 84
Divide each side by 3.
y = 28
Substitute 28 for y in (2).
(2)-----> x = 2(28) + 6
x = 56 + 6
x = 62
So, the two angles are 62° and 28°.
Problem 7 :
Find the value of x :
Solution :
From the picture above, it is clear that the angles x and 2x are complementary.
Then,
x + 2x = 90
Simplify.
3x = 90
Divide each side by 3.
x = 30
So, the value of x is 30.
Problem 8 :
Find the value of x :
Solution :
From the picture above, it is clear that the angles (x+1), (x-1) and (x+3) are complementary.
Then,
(x+1) + (x-1) + (x+3) = 90
x + 1 + x - 1 + x + 3 = 90
Simplify.
3x + 3 = 90
Subtract 3 from each side.
3x = 87
Divide each side by 3.
x = 29
So, the value of x is 29.
Problem 9 :
Find the value of x :
Solution :
From the picture above, it is clear that (2x+3) and (x-6) are supplementary angles.
Then,
(2x+3) + (x-6) = 180
2x + 3 + x - 6 = 180
Simplify.
3x - 3 = 180
Add 3 to each side.
3x = 183
Divide each side by 3.
x = 61
So, the value of x is 61.
Problem 10 :
Find the value of x :
Solution :
From the picture above, it is clear (5x+4), (x-2) and (3x+7) are supplementary angles.
Then,
(5x+4) + (x-2) + (3x+7) = 180
5x + 4 + x -2 + 3x + 7 = 180
Simplify.
9x + 9 = 180
Subtract 9 from each side.
9x = 171
Divide each side by 9.
x = 19
So, the value of x is 19.
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