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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° =

1 answer

To determine the equation for the angle measures, we start by knowing the angles formed at point B:

  • Angle A B C measures 90 degrees.
  • Angle A B D measures 4x degrees.
  • Angle D B C measures (7x - 9) degrees.

Since angles A B D and D B C, along with angle A B C, make up the 90 degrees at point B, we can set up the equation:

\[ \text{Angle A B D} + \text{Angle D B C} = \text{Angle A B C} \]

Substituting the angle measures into the equation, we have:

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

This equation represents the relationship between the angles around point B. You can simplify it further to solve for x if needed.

In the format requested, your placeholder equation could be:

(4x)° + (7x - 9)° = 90°.