For two vertical angles with measures m∠1=(2x+26)° and m∠3=(3x+32)° , what is the measure of each angle ?(1 point) °
Vertical angles are always congruent, meaning they have the same measure. Therefore, m∠1 = m∠3.
Since m∠1 = (2x + 26)° and m∠3 = (3x + 32)°, we can set them equal to each other:
(2x + 26)° = (3x + 32)°
To solve for x, first, we can subtract 2x from both sides of the equation:
26° = (3x + 32 - 2x)°
This simplifies to:
26° = (x + 32)°
Next, subtract 32° from both sides:
26° - 32° = (x + 32 - 32)°
-6° = x°
Therefore, x = -6.
To find the measure of each angle, we can substitute x = -6 into the expressions for m∠1 and m∠3:
m∠1 = (2x + 26)° = (2(-6) + 26)° = (12 + 26)° = 38°
m∠3 = (3x + 32)° = (3(-6) + 32)° = (-18 + 32)° = 14°
Thus, the measure of each angle is m∠1 = 38° and m∠3 = 14°.
so whats the answer
The measures of the two vertical angles are:
m∠1 = 38°
m∠3 = 14°