Asked by mushroom

Two adjacent angles are inside a 90 degree angle. One angle has a measure of (x + 4) degrees and the other angle has a measure of (3x + 2) degrees. What is x?
Answered by mushroom
two adjacent angles form a resulting angle with measure 160 degrees. m <1 = 3x and m<2 = (2x + 10) degrees. solve for x. what are the two unknown angles' measurments?
Answered by mushroom
an illustration shows three rays extending from a common origin. the angle measures between them are labeled. what are the two unknown angle measures that for the 90 degree angle?

first angle: (x + 4) degrees.
second angle: (3x + 2) degrees.

answer:
(x + 4) degrees = ___ degrees,
(3x + 2) degrees = ___ degrees.
Answered by GPT 3.5
The sum of the two adjacent angles must be equal to 90 degrees, so we have the equation (x + 4) + (3x + 2) = 90.
Combining like terms, we have 4x + 6 = 90.
Subtracting 6 from both sides, we have 4x = 84.
Dividing both sides by 4, we have x = <<21=21>>21. Answer: \boxed{21}.
Answered by GPT 3.5
Since we have two adjacent angles, the sum of their measures must equal the measure of the resulting angle. Therefore, we have the equation 3x + (2x + 10) = 160.
Combining like terms, we have 5x + 10 = 160.
Subtracting 10 from both sides, we have 5x = 150.
Dividing both sides by 5, we have x = 30.
Therefore, m <1 = 3x = 3(30) = 90 degrees.
And m <2 = 2x + 10 = 2(30) + 10 = 60 + 10 = 70 degrees.
So, the measure of angle 1 is 90 degrees and the measure of angle 2 is 70 degrees.
Answered by GPT 3.5
To find the two unknown angle measures that form the 90 degree angle, we need to set up an equation based on the fact that the sum of the two unknown angles and the given angle must be equal to 90 degrees.

The given angle measure is (x + 4) degrees and the second angle measure is (3x + 2) degrees.

The unknown angle measures are labeled as (x) degrees and (y) degrees.

We can create the equation: (x + 4) + (3x + 2) + (y) = 90.

Combining like terms, we have: 4x + 6 + y = 90.

To solve for the unknown angle measures (x) and (y), we need an additional equation or more information.