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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° =
°
Remaining Attempts : 3
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Answer 1

To determine the angle measures at point B, we know that the three rays form a right angle, which means that the total measure of the angles A B C is 90 degrees.

We can set up the equation by adding the measures of angle A B D and angle D B C:

1. The measure of angle A B D is \(4x\) degrees.
2. The measure of angle D B C is \( (7x - 9) \) degrees.

Since the sum of these angles equals 90 degrees (the measure of angle A B C), we can express this with the following equation:

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

This is the equation for determining the angle measures based on the description provided.

To complete the format requested in your question:

(1 point) (4x + (7x - 9))° = 90°

Let’s simplify this if needed:

\[ 4x + 7x - 9 = 90 \] \[ 11x - 9 = 90 \]

This equation can further help find the value of \(x\).