Regular pentagonal tiles and triangular tiles are arranged in the pattern shown. The pentagonal tiles are all the same size and

Question

Juli2301

2 months ago

9

Regular pentagonal tiles and triangular tiles are arranged in the pattern shown. The pentagonal tiles are all the same size and

shape and triangular tiles are all the same size and shape. Find the angle measures of the triangular tiles.

Mathematics

1 answer:

zzz [12.3K] · Answer 1 · 2026-03-16T22:20:40+03:00

Initially, you must determine the unknown measurements. The actual angle measurements in the hexagon are not specified; however, an expression is provided. First, solve for x to substitute it into the angle measurement. You should set the two provided sides equal: 20x+48=33x+9. After finding x, use it to calculate each angle measurement, leading to 108. Since the hexagon is regular, all angles are equal. Observing the angle at the top exposes two triangles and the angle itself. As it forms a straight line, the total equals 180. You already know the hexagon's angle measurement and lack the triangle measurements. Therefore, 180-108=72. The missing angle part is 72. To find each triangle's angle measurement, divide this by 2, resulting in 36 degrees.