∠Q
and  ∠R
are complementary. The measure of  ∠Q
is 26° less than the measure of  ∠R.
Find the measure of each angle.

Let's denote the measure of \(\angle R\) as \(x\).

Since \(\angle Q\) is 26° less than \(\angle R\), the measure of \(\angle Q\) can be expressed as \(x - 26^\circ\).

Given that \(\angle Q\) and \(\angle R\) are complementary, their sum is 90°. Therefore, we can set up the equation:

\[
x + (x - 26^\circ) = 90^\circ
\]

Simplifying the equation:

\[
2x - 26^\circ = 90^\circ
\]

Add 26° to both sides:

\[
2x = 116^\circ
\]

Now, divide by 2 to solve for \(x\):

\[
x = 58^\circ
\]

So, the measure of \(\angle R\) is 58°. 

To find \(\angle Q\):

\[
\angle Q = x - 26^\circ = 58^\circ - 26^\circ = 32^\circ
\]

Thus, the measures of the angles are:
- \(\angle Q = 32^\circ\)
- \(\angle R = 58^\circ\)

Would you like more details or have any questions?

Here are 5 related questions:
1. What are supplementary angles?
2. If \(\angle Q\) were 40°, what would be \(\angle R\)?
3. How do you solve for unknown angles in a triangle?
4. What happens if two angles are both 45°?
5. Can complementary angles be more than 90° in total?

**Tip:** Always double-check your work by adding the calculated angles to ensure they meet the conditions given, such as being complementary or supplementary.

Learn how to find the measures of complementary angles ∠Q and ∠R where ∠Q is 26° less than ∠R. This problem involves basic geometry concepts and complementary angles. Suitable for students in Grades 6-8.

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