12. The sum of the measures of two complementary angles is 90°
. If one angle measures
15° more than twice the measure of its complement, find the measure of each angle

Let's define the angles in terms of a variable.

Let:
- \( x \) = the measure of one angle.
- \( 90^\circ - x \) = the measure of its complement (since complementary angles sum up to \( 90^\circ \)).

According to the problem, one angle is 15° more than twice the measure of its complement. This gives the equation:

\[
x = 2(90^\circ - x) + 15^\circ
\]

### Step-by-step solution:
1. Expand the equation:
\[
x = 180^\circ - 2x + 15^\circ
\]
\[
x = 195^\circ - 2x
\]

2. Add \( 2x \) to both sides to move all \( x \)-terms to one side:
\[
x + 2x = 195^\circ
\]
\[
3x = 195^\circ
\]

3. Solve for \( x \):
\[
x = \frac{195^\circ}{3} = 65^\circ
\]

Thus, the first angle measures \( 65^\circ \).

4. To find the complement, subtract \( 65^\circ \) from \( 90^\circ \):
\[
90^\circ - 65^\circ = 25^\circ
\]

### Final Answer:
- The first angle is \( 65^\circ \).
- The complement is \( 25^\circ \).

Would you like further details or have any questions?

Here are 5 related questions:
1. What are supplementary angles and how do they differ from complementary angles?
2. How would you solve this problem if the condition involved supplementary angles?
3. Can you express complementary angles using different algebraic equations?
4. How can we verify the solution of this complementary angle problem?
5. What are the applications of complementary angles in geometry?

**Tip:** Always verify your solution by plugging the angles back into the original conditions to ensure they satisfy all given relations.

The sum of the measures of two complementary angles is 90°. If one angle measures 15° more than twice the measure of its complement, find the measure of each angle.

This problem involves complementary angles, where the sum of two angles equals 90°. Learn how to solve for the measures of two angles when one is 15° more than twice the measure of its complement using algebra and linear equations. Suitable for students in Grades 6-8.

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