∠1 and angle, 2∠2 are supplementary angles. If m, angle, 1, equals, left parenthesis, 7, x, minus, 20, right parenthesis, degreesm∠1=(7*x*−20)∘ and m, angle, 2, equals, left parenthesis, 2, x, minus, 7, right parenthesis, degreesm∠2=(2*x*−7)∘, then find the measure of angle, 2∠2.

Supplementary angles are two angles whose measures add up to 180 degrees. In this case, you are given the following information:

- \( m\angle 1 = (7x - 20)^\circ \)
- \( m\angle 2 = (2x - 7)^\circ \)

Since \( \angle 1 \) and \( \angle 2 \) are supplementary, we know:

\[
m\angle 1 + m\angle 2 = 180^\circ
\]

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

\[
(7x - 20) + (2x - 7) = 180
\]

Now, simplify the equation:

\[
7x - 20 + 2x - 7 = 180
\]
\[
9x - 27 = 180
\]

Next, add 27 to both sides:

\[
9x = 207
\]

Now, solve for \( x \):

\[
x = \frac{207}{9} = 23
\]

Now that we have \( x = 23 \), we can find the measure of \( m\angle 2 \):

\[
m\angle 2 = 2x - 7 = 2(23) - 7 = 46 - 7 = 39^\circ
\]

Thus, the measure of \( \angle 2 \) is \( 39^\circ \).

Would you like further clarification on any step?

Here are 5 related questions to explore:
1. What is the measure of \( \angle 1 \) based on this solution?
2. What is the definition of complementary angles, and how do they differ from supplementary angles?
3. How do you solve for unknowns in other geometric scenarios, such as complementary angles?
4. Can you find examples where angles form linear pairs, and how do they relate to supplementary angles?
5. How do the properties of parallel lines intersected by a transversal help solve for angle measures?

**Tip:** Always check if angles are complementary, supplementary, or part of a linear pair when solving for unknowns in geometric problems.

∠1 and ∠2 are supplementary angles. If m∠1 = (7x − 20)° and m∠2 = (2x − 7)°, then find the measure of ∠2.

Solve for the measure of angle 2 when two angles are supplementary. This problem uses algebraic equations with expressions for angle measures in terms of x. Suitable for students in Grades 8-10.

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