Use the image to answer the question.

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° = __°

Answer 1

To find the equation for determining the angle measures, we start by observing that angle ABC measures 90 degrees, which is the sum of angle ABD and angle DBC.

Given:

• Angle A B D = 4x degrees
• Angle D B C = (7x - 9) degrees

Since angle A B C forms a right angle (90 degrees), we can write the equation:

\[ AB + BD = ABC \]

That is, we can set it up as:

\[ (4x) + (7x - 9) = 90 \]

Thus, we need to express it in the form provided in your question:

\[ (4x)° + (7x - 9)° = 90° \]

So the equation can be presented as:

(4x)° + (7x - 9)° = 90°

In the format requested: (4x)° + (7x - 9)° = 90°.