 the measure of one angle of a right triangle is 30° more than the measure of thesmallest angle, then the measure of the smallest angle is

Let's denote the measure of the smallest angle of the right triangle as \(x\). 

Since the triangle is a right triangle, one of its angles is \(90^\circ\). The other two angles, including the smallest angle, must add up to \(90^\circ\) because the sum of all angles in a triangle is \(180^\circ\).

Given that one angle is \(30^\circ\) more than the smallest angle, we can denote the larger of the two remaining angles as \(x + 30^\circ\).

Now, we can set up the equation:

\[
x + (x + 30^\circ) = 90^\circ
\]

Simplify the equation:

\[
2x + 30^\circ = 90^\circ
\]

Subtract \(30^\circ\) from both sides:

\[
2x = 60^\circ
\]

Divide by 2:

\[
x = 30^\circ
\]

So, the measure of the smallest angle is **30 degrees**.

### Conclusion:
The smallest angle of the right triangle is \(30^\circ\).

Would you like further details or have any questions about this solution?

Here are 5 related questions for further exploration:
1. What is the measure of the largest angle in a right triangle?
2. How do you find the length of the sides in a right triangle given one angle?
3. What is the sine, cosine, and tangent of a \(30^\circ\) angle?
4. How does the Pythagorean Theorem relate to the angles of a right triangle?
5. How can you determine the area of a right triangle given two side lengths?

**Tip:** Remember, in any triangle, the sum of all angles is always \(180^\circ\).

The measure of one angle of a right triangle is 30° more than the measure of the smallest angle. What is the measure of the smallest angle?

Discover how to calculate the smallest angle in a right triangle when one angle is 30° more than the other. This detailed guide explains key geometric concepts and formulas, making it ideal for students in Grades 6-8.

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