An illustration shows three rays extending from a common origin. The angle measures between them are labeled.

Question

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

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

Answer 1

To find the two unknown angle measures that form the 90° angle, we will set up the following equation based on the sum of angles.

If we have two angles, $(x+4)°$ and $(3x+2)°$, and together these angles sum up to 90 degrees, we can form the equation:

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

Now, simplify the equation:

$$x+4+3x+2=90$$

$$4x+6=90$$

Next, subtract 6 from both sides:

$$4x=90-6$$ $$4x=84$$

Now, divide both sides by 4:

$$x=\frac{84}{4}$$ $$x=21$$

Now we can substitute $x$ back into the expressions for the angles:

1. For $(x+4)°$: $$(21+4)°=25°$$

2. For $(3x+2)°$: $$(3\cdot 21+2)°=(63+2)°=65°$$

So, the two unknown angle measures that form the 90° angle are:

$$(x+4)°=25°,(3x+2)°=65°$$