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° =
°
What is the equation for determining the angle measures?
(1 point)
(
)° + 4x° =
°
Answers
GPT-4o mini
To determine the angle measures in the given situation, we know that angles \( \angle ABC \), \( \angle ABD \), and \( \angle DBC \) together form a right angle at point B, which measures \( 90^\circ \).
Given:
- \( \angle ABC = 90^\circ \)
- \( \angle ABD = 4x^\circ \)
- \( \angle DBC = (7x - 9)^\circ \)
Since \( A, D, \) and \( C \) form a right angle at B, we can set up the equation based on the sum of angles. The equation will be:
\[
\angle ABD + \angle DBC = \angle ABC
\]
Substituting the values we have:
\[
4x + (7x - 9) = 90
\]
This creates the equation for determining the angle measures. The simplified equation based on your prompt would be:
\[
4x + (7x - 9) = 90
\]
This can be rearranged as:
\[
4x + 7x - 9 = 90
\]
So, the concise representation for the equation based on your format is:
\[
(4x)° + (7x - 9)° = 90°
\]
Given:
- \( \angle ABC = 90^\circ \)
- \( \angle ABD = 4x^\circ \)
- \( \angle DBC = (7x - 9)^\circ \)
Since \( A, D, \) and \( C \) form a right angle at B, we can set up the equation based on the sum of angles. The equation will be:
\[
\angle ABD + \angle DBC = \angle ABC
\]
Substituting the values we have:
\[
4x + (7x - 9) = 90
\]
This creates the equation for determining the angle measures. The simplified equation based on your prompt would be:
\[
4x + (7x - 9) = 90
\]
This can be rearranged as:
\[
4x + 7x - 9 = 90
\]
So, the concise representation for the equation based on your format is:
\[
(4x)° + (7x - 9)° = 90°
\]
what_she _did _it_again
the answer is (7x-9)+4r=90