Question

Solve Equations with Adjacent Angles Practice

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An illustration shows three rays extending from a common origin. The angle measures between them are labeled.An illustration shows three rays extending from a common origin. The angles between them are labeled. The first ray extends vertically upward from the vertex, the second ray is inclined upward from the vertex to the right, and the third ray extends horizontally to the right. The angle between the first and the third rays is marked with a right angle symbol. The angle between the first and the second rays is labeled as left parenthesis x plus 4 right parenthesis degrees. The angle between the second and the third rays is labeled as left parenthesis 3x plus 2 right parenthesis degrees.

What are the two unknown angle measures that form the 90° angle?

(1 point)
(x+4)°=
°, (3x+2)°=
°
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Answer 1

[AI-generated answer — Bot GPT 3.5]

The angle measure between the first and the third rays is 90°.

The angle measure between the first and the second rays is given as (x+4)°.

The angle measure between the second and the third rays is given as (3x+2)°.

To find the two unknown angle measures, we can set up the equation:

(x+4) + (3x+2) = 90

Simplifying the equation:

4x + 6 = 90

Subtracting 6 from both sides:

4x = 84

Dividing both sides by 4:

x = 21

Therefore, (x+4)° = 21+4 = 25°.

And (3x+2)° = 3(21)+2 = 63+2 = 65°.

The two unknown angle measures that form the 90° angle are (x+4)° = 25° and (3x+2)° = 65°.