The measures of two supplementary angles are 6y + 3 and 4y - 13. Find the measures of the angles.
Select one:
a. 117 and 63
b. 19
c. 63 and 27
d. 10
Two angles are complementary. One angle measures 26 degrees more than the other. Find the measure of the two angles.
Select one:
a. 77 and 103
b. 32 and 58
c. 167 and 193
d. 76 and 104
We'll be glad to check your answers.
Be sure you know what complementary and supplementary angles are.
1)
6 y + 3° is first angle
4 y - 13° is second angle
6 y + 3° + 4 y - 13° = 180°
10 y - 10° = 180°
10 y = 180° + 10°
10 y = 190°
y = 190° / 10
y = 19°
6 y + 3° = 6 ∙ 19° + 3° = 114° + 3° = 117°
4 y - 13° = 4 ∙ 19° - 13° = 76° - 13° = 63°
117° and 63°
2)
x is first angle
x + 26° is second angle
x + x + 26° = 90°
2 x + 26° = 90°
2 x = 90° - 26°
2 x = 64°
x = 64° / 2
x = 32°
32° is first angle
x + 26° = 32° + 26° = 58° is second angle
32° and 58°
To find the measures of two supplementary angles, we need to set up an equation and solve for the variable.
Supplementary angles add up to 180 degrees. So, we can set up the equation:
(6y + 3) + (4y - 13) = 180
Combine like terms:
10y - 10 = 180
Add 10 to both sides of the equation:
10y = 190
Divide both sides by 10:
y = 19
Now that we have the value of y, we can substitute it into the expressions for the angles:
Angle 1 = 6y + 3 = (6 * 19) + 3 = 117
Angle 2 = 4y - 13 = (4 * 19) - 13 = 63
Therefore, the measures of the angles are 117 degrees and 63 degrees. Hence, the correct answer is option a: 117 and 63.
Now let's work on the second problem.
If two angles are complementary, they add up to 90 degrees. We can set up an equation to find the measures of the angles.
Let the measure of one angle be x degrees. The other angle measures 26 degrees more, so it is x + 26 degrees.
Now, we can set up the equation:
x + (x + 26) = 90
Combine like terms:
2x + 26 = 90
Subtract 26 from both sides of the equation:
2x = 64
Divide both sides by 2:
x = 32
Now that we have the value of x, we can substitute it into the expressions for the angles:
Angle 1 = x degrees = 32 degrees
Angle 2 = x + 26 degrees = 32 + 26 = 58 degrees
Therefore, the measures of the two angles are 32 degrees and 58 degrees. Hence, the correct answer is option b: 32 and 58.