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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° =
°

2 answers

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:

\[ (4x)° + (7x - 9)° = 90° \]

the answer is (7x-9)+4r=90