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 determine the equation for the angle measures, we can use the information given about the angles formed at point B.

We know that the angles A B C, A B D, and D B C add up to 90 degrees, since they form a right angle at point B.

Given the measures:

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

The equation that shows the sum of angles A B D and D B C equals the total angle A B C (which is 90 degrees) can be set up as follows:

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

Therefore, the specific equation for determining the angle measures is:

(7x - 9)° + 4x° = 90°.