∠1 and angle, 2∠2 are complementary angles. If m, angle, 1, equals, left parenthesis, 2, x, minus, 26, right parenthesis, degreesm∠1=(2x−26) 
∘
  and m, angle, 2, equals, left parenthesis, 4, x, minus, 28, right parenthesis, degreesm∠2=(4x−28) 
∘
 , then find the measure of angle, 2∠2.

We are given that ∠1 and ∠2 are complementary angles. This means their sum is 90°. The expressions for their measures are:

\[
m∠1 = (2x - 26)^\circ
\]
\[
m∠2 = (4x - 28)^\circ
\]

Since they are complementary, we can set up the equation:

\[
m∠1 + m∠2 = 90^\circ
\]

Substitute the expressions for \(m∠1\) and \(m∠2\):

\[
(2x - 26) + (4x - 28) = 90
\]

Now, simplify the equation:

\[
6x - 54 = 90
\]

Add 54 to both sides:

\[
6x = 144
\]

Divide by 6:

\[
x = 24
\]

Now, substitute \(x = 24\) into the expression for \(m∠2\):

\[
m∠2 = 4x - 28 = 4(24) - 28 = 96 - 28 = 68^\circ
\]

Thus, the measure of ∠2 is **68°**.

Would you like further clarification or details?

Here are some related questions:
1. How can you verify if two angles are complementary?
2. What happens if the sum of two angles is greater than 90°?
3. How do you solve for the value of \(x\) in complementary angle problems?
4. What is the relationship between supplementary and complementary angles?
5. How do we classify angles based on their measures?

**Tip:** In complementary angle problems, always remember their sum equals 90°, which simplifies finding unknowns.

∠1 and ∠2 are complementary angles. If m∠1 = (2x - 26)° and m∠2 = (4x - 28)°, then find the measure of ∠2.

Learn how to solve for the measure of ∠2 when ∠1 and ∠2 are complementary angles. Using algebraic equations and complementary angle theorem, this solution breaks down the steps for solving expressions like m∠1 = (2x - 26)° and m∠2 = (4x - 28)°. Suitable for students in Grades 8-10.

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