1. If two angles are complementary angles and their measure are (x + 5) and (5x+13)º respectively. Find x and the
measure of each angle.
2. If two angles are supplementary and their measures are (5x + 10) and (x+14)º respectively. Find x and the measure
of each angle.
3. If two angles are vertical and their measures are (13x + 5) and (6x + 26) º respectively. Find x and the measure of
each angle.
4. If two angles are supplementary and their measures are (12x+13) and (3x+17) respectively. Find x and the
measure of each angle.
5. If two angles are complementary angles and they measure (3x + 6) and (4x + 7)
respectively. Find x and the measure
of each angle.
6. Find the measures of the complementary angle of a 120 angle less than twice the other.
7. The measure of the supplement of an angle is 250 more than 4 times the measure of the angle. Find the measure of
each angle.
measure of each angle.
2. If two angles are supplementary and their measures are (5x + 10) and (x+14)º respectively. Find x and the measure
of each angle.
3. If two angles are vertical and their measures are (13x + 5) and (6x + 26) º respectively. Find x and the measure of
each angle.
4. If two angles are supplementary and their measures are (12x+13) and (3x+17) respectively. Find x and the
measure of each angle.
5. If two angles are complementary angles and they measure (3x + 6) and (4x + 7)
respectively. Find x and the measure
of each angle.
6. Find the measures of the complementary angle of a 120 angle less than twice the other.
7. The measure of the supplement of an angle is 250 more than 4 times the measure of the angle. Find the measure of
each angle.
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Answer:
1.x = 8, the angles are 13º and 57º
2.x = 12, the angles are 146º and 34º
3.x = 3, the angles are 68º and 97º
4.x = 6, the angles are 115º and 65º
5.x = 7, the angles are 27º and 63º
6.The angles are 30º and 60º
7.The angle measures 58º, its supplement measures 302º.
Answer:
Complementary angles are two angles whose measures add up to 90 degrees.
Let's set up an equation using the given information:
(x + 5) + (5x + 13) = 90
Simplifying the left side of the equation:
6x + 18 = 90
Subtracting 18 from both sides:
6x = 72
Dividing both sides by 6:
x = 12
Now that we know x, we can find the measure of each angle:
The first angle is x + 5, so substituting in x = 12:
x + 5 = 12 + 5 = 17
Therefore, the measure of the first angle is 17 degrees.
The second angle is 5x + 13, so substituting in x = 12:
5x + 13 = 5(12) + 13 = 73
Therefore, the measure of the second angle is 73 degrees.
So the two complementary angles are 17 degrees and 73 degrees.
2. Supplementary angles add up to 180 degrees. So, we can set up the equation:
(5x + 10) + (x + 14) = 180
Simplifying the left-hand side of the equation, we get:
6x + 24 = 180
Subtracting 24 from both sides, we get:
6x = 156
Dividing both sides by 6, we get:
x = 26
Now that we know the value of x, we can find the measures of the angles:
First angle: 5x + 10 = 5(26) + 10 = 140 degrees
Second angle: x + 14 = 26 + 14 = 40 degrees
Therefore, the two angles are 140 degrees and 40 degrees, and x is equal to 26.
3.Vertical angles are a pair of non-adjacent angles formed by two intersecting lines. Vertical angles are always congruent, which means they have the same measure. So we can set up the equation:
13x + 5 = 6x + 26
Simplifying the left-hand side of the equation, we get:
7x = 21
Dividing both sides by 7, we get:
x = 3
Now that we know the value of x, we can find the measures of the angles:
First angle: 13x + 5 = 13(3) + 5 = 44 degrees
Second angle: 6x + 26 = 6(3) + 26 = 44 degrees
Therefore, the two angles are both 44 degrees, and x is equal to 3.