State the theorem or postulate that is related to the measures of the angles in each pair. Then find the angle measures.

m∠3=(23x+11)°,m∠4=(14x+21)°

Can you teach me this problem??
Please...

Since I have no idea of the diagram, it's hard to say.

But I suspect you are dealing with angles on a transversal of parallel lines. Check into adjacent, alternate interior/exterior, etc.

To find the angle measures, we need to use the theorem or postulate related to the measures of the angles in each pair.

In this case, we can use the Vertical Angles Theorem, which states that vertical angles are congruent. In other words, if two angles are vertical angles, they have the same measure.

So, since angle 3 and angle 4 are vertical angles, we can set up the equation:

m∠3 = m∠4

(23x + 11)° = (14x + 21)°

Now, we can solve for x. Rearranging the equation, we have:

23x + 11 = 14x + 21

Subtracting 14x from both sides, we get:

9x + 11 = 21

Next, subtract 11 from both sides:

9x = 10

Dividing both sides by 9, we have:

x = 10/9

Now that we have the value of x, we can substitute it back into the original equations to find the angle measures.

m∠3 = (23x + 11)°

m∠3 = (23 * (10/9) + 11)°

Simplifying,

m∠3 = (230/9 + 99/9)°

m∠3 = (329/9)°

Therefore, the measure of angle 3 is 329/9 degrees.

Similarly, we can find the measure of angle 4:

m∠4 = (14x + 21)°

m∠4 = (14 * (10/9) + 21)°

Simplifying,

m∠4 = (140/9 + 189/9)°

m∠4 = (329/9)°

Hence, the measure of angle 4 is also 329/9 degrees.

Certainly! This problem involves finding the measures of angles in a pair. To do this, we'll use the Angle Sum Theorem.

The Angle Sum Theorem states that the sum of the measures of the angles in any triangle is always equal to 180 degrees.

In this case, we have two angles: ∠3 and ∠4. We'll set up an equation using the Angle Sum Theorem to find the value of x that corresponds to these angles.

According to the theorem, we can write the equation as follows:
m∠3 + m∠4 = 180 degrees

Substituting the given expressions for the angle measures, we get:
(23x + 11) + (14x + 21) = 180

Now, we can solve this equation to find the value of x. Let's proceed step by step:

Combine like terms:
37x + 32 = 180

Subtract 32 from both sides:
37x = 148

Divide by 37 on both sides:
x = 4

Now that we have the value of x, we can substitute it back into the expressions for the angle measures to find their actual values.

For ∠3:
m∠3 = (23x + 11)
= (23 * 4 + 11)
= 92 + 11
= 103 degrees

For ∠4:
m∠4 = (14x + 21)
= (14 * 4 + 21)
= 56 + 21
= 77 degrees

Therefore, the measure of ∠3 is 103 degrees, and the measure of ∠4 is 77 degrees.

I hope this explanation helps you understand how to approach and solve this problem!