For two vertical angles with measures m∠1=(2x+26)° and m∠3=(3x+32)° , what is the measure of each angle?

Answer 1

Vertical angles are formed when two lines intersect. They are always congruent, which means they have the same measure.

In this case, we have two vertical angles with measures m∠1=(2x+26)° and m∠3=(3x+32)°.

Therefore, we can set up an equation: (2x+26)° = (3x+32)°.

Now, we can solve for x:

2x+26 = 3x+32

Subtract 2x from both sides:

26 = x+32

Subtract 32 from both sides:

-6 = x

Now, we can substitute this value of x back into either of the expressions for the angles to find their measures.

Let's substitute it into m∠1=(2x+26)°:

m∠1 = 2(-6)+26
= -12+26
= 14

Thus, the measure of angle 1 is 14°.

Since vertical angles are congruent, the measure of angle 3 will also be 14°.

Answer 2

In a diagram, ∠A and ∠B are vertical angles, and ∠B is a complementary angle with ∠C . If m∠A=22° , write an equation that you can use to solve for m∠C .(2 points)