Solve Equations with Adjacent Angles Practice%0D%0AComplete this assessment to review what you've learned. It will not count toward your grade.%0D%0A5 of 55 of 5 Items%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0AQuestion%0D%0AUse the image to answer the question.%0D%0A%0D%0AAn illustration shows three rays extending from a common origin. The angle measures between them are labeled.%0D%0A%0D%0AWhat are the two unknown angle measures that form the 90°%0D%0A90%0D%0A°%0D%0A angle?%0D%0A%0D%0A(1 point)%0D%0A(x+4)°=%0D%0A(%0D%0A%0D%0A+%0D%0A4%0D%0A)%0D%0A°%0D%0A=%0D%0A °%0D%0A°%0D%0A, (3x+2)°=%0D%0A(%0D%0A3%0D%0A%0D%0A+%0D%0A2%0D%0A)%0D%0A°%0D%0A=%0D%0A °

1 answer

To find the two unknown angle measures that form the 90° angle, we can set up an equation using the fact that the sum of adjacent angles is equal to 90°.

Let's say the two unknown angle measures are (x+4)° and (3x+2)°.

According to the given information, the sum of these two angles is 90°.

So, the equation we can set up is:

(x+4)° + (3x+2)° = 90°

To solve this equation, we combine like terms:

4x + 6 = 90

Next, we isolate the variable:

4x = 90 - 6

4x = 84

Finally, we solve for x by dividing both sides of the equation by 4:

x = 84/4

x = 21

Now that we know the value of x, we can substitute it back into the original expressions to find the angle measures:

(x+4)° = 21 + 4 = 25°

(3x+2)° = 3(21) + 2 = 63 + 2 = 65°

Therefore, the two unknown angle measures that form the 90° angle are 25° and 65°.