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)° = 90°
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 know that the sum of the two complementary angles is equal to 90 degrees.
Therefore, we have the equation:
(4x)° + (2x)° = 90°
Combine like terms:
6x° = 90°
Divide both sides by 6:
x = 15
Now we can substitute the value of x back into the expressions for the angle measures:
(4x)° = (4 * 15)° = 60°
(2x)° = (2 * 15)° = 30°
Therefore, the value of x is 15, the measure of the first angle is 60 degrees, and the measure of the second angle is 30 degrees.
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, we know that the sum of two complementary angles is equal to 90 degrees.
Therefore, we have the equation:
36° + (x - 3)° = 90°
Combine like terms:
x - 3 + 36 = 90
x + 33 = 90
Subtract 33 from both sides:
x = 57
Now we can substitute the value of x back into the expression for the unknown angle measure:
Unknown angle measure = (57 - 3)° = 54°
Therefore, the value of x is 57 and the unknown angle measure is 54 degrees.