For two vertical angles where ∠1=2x+26° and ∠3=3x−32°, what is the measure of each angle?
Sorry, Damon, but you need to review the definition of vertical angles.
vertical angles are congruent, so
2x+26 = 3x−32
x = 58
so each angle is 142°
To find the measure of each angle, we need to set the two expressions equal to each other since vertical angles are congruent.
So, we have:
∠1 = ∠3
2x + 26° = 3x - 32°
To isolate the x term, let's subtract 2x from both sides of the equation:
2x - 2x + 26° = 3x - 2x - 32°
26° = x - 32°
Now, let's add 32° to both sides of the equation to isolate x:
26° + 32° = x - 32° + 32°
58° = x
Now that we know the value of x, we can substitute it back into one of the original expressions to find the measure of the angles.
Let's substitute x = 58° into ∠1:
∠1 = 2x + 26°
∠1 = 2(58°) + 26°
∠1 = 116° + 26°
∠1 = 142°
Similarly, let's substitute x = 58° into ∠3:
∠3 = 3x - 32°
∠3 = 3(58°) - 32°
∠3 = 174° - 32°
∠3 = 142°
Therefore, the measure of both angles ∠1 and ∠3 is 142°.
∠1 = 2x + 26°
∠3 = 3x - 32°
angle 1 - angle 3 = 90 deg or 270
2 x + 26 - 3 x + 32 = 90
-x + 58 = 90
- x = 32
x = -32
A1 = 2 x+26 = -64 + 26 = - 38
A3 = 3 x - 32 = -128
yes difference is 90 deg
try the other choice as well