Solve Equations with Complementary Angles Practice
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Question
Use the image to answer the question.
An illustration shows three rays A, D, and C emerging from a point labeled B, forming a right angle at B. The right angle is divided into two parts by ray B D. The angles face leftward. Angle A B C measures 90 degree, angle A B D measures 4 x degrees, and angle D B C measures left parenthesis 7 x minus 9 right parenthesis degrees.
What is the equation for determining the angle measures?
(1 point)
(
)° + 4x° =
°
90° + 4x° = (7x - 9)°
Two complementary angles have measures (4x)° and (2x)° . What is the value of x and the two angle measures?(2 points)
x=
, (4x)°=
°, and (2x)°=
°
To find the value of x, we can set up an equation using the fact that the two angles are complementary:
(4x)° + (2x)° = 90°
Combining like terms, we have:
6x° = 90°
Dividing both sides by 6, we find:
x = 15°
Plugging this value back into the equations for the angle measures:
(4x)° = (4 * 15)° = 60°
(2x)° = (2 * 15)° = 30°
So, x = 15°, (4x)° = 60°, and (2x)° = 30°.
In a figure, one complementary angle has a measure of 36° and the other has a measure of (x−3)° . What is the value of x and the value of the unknown angle measure?(1 point)
x=
, unknown angle measure =
°
To find the value of x and the unknown angle measure, we can set up an equation using the fact that the two angles are complementary:
36° + (x-3)° = 90°
Now, we can solve for x by subtracting 36° from both sides and then adding 3° to both sides:
x - 3° = 90° - 36°
x - 3° = 54°
x = 54° + 3°
x = 57°
Now, we can find the value of the unknown angle measure by substituting the value of x back into the equation:
Unknown angle measure = x - 3° = 57° - 3° = 54°
So, x = 57° and the unknown angle measure is 54°.