EREIDHAS MATH Mhautad \#17 Chech Usten Find the measure of each acute angle in a right triangle where the measure of one acute angle is 8 times the measure of the other acute angle. The smaller acute angles measures \( \square \) \( { }^{\circ} \) and the larger acute angle measures \( \square \)。

In a right triangle, the two acute angles must sum to 90 degrees. If we let the smaller acute angle be \( x \), then the larger angle is \( 8x \). Setting up the equation, we get: \( x + 8x = 90 \) This simplifies to: \( 9x = 90 \) So, \( x = 10 \) degrees. Therefore, the smaller acute angle measures \( 10^\circ \) and the larger acute angle measures \( 80^\circ \). Now, here's a fun fact: The concept of angles and triangles can be traced back to ancient civilizations such as the Greeks, who studied geometry extensively. Figures like Euclid laid the groundwork for geometric properties that are still taught in schools today! As for real-world applications, understanding the properties of triangles is crucial in fields like architecture, engineering, and even art. For instance, architects use triangles in design to create stable structures, because a triangle's shape doesn't change if you push on it, unlike quadrilaterals which can distort easily.