Answered

At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Get quick and reliable solutions to your questions from a community of experienced professionals on our platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

The middle angle in a triangle is 4 times the measure of the smallest angle. The smallest angle is the difference of the largest angle and the middle angle. Find the measures of the three angles.

Find the smallest angle, largest angle, and middle angle in degrees

Sagot :

sqdancefan

Answer:

  • smallest: 18°
  • largest: 90°
  • middle: 72°

Step-by-step explanation:

We can solve this using the relationship between the angles together with the angle sum theorem. Let s represent the measure of the smallest angle. Then the middle angle is 4s, and the largest angle is (4s +s). The angle sum theorem tells us the sum of angles in a triangle is 180°.

  smallest + middle + largest = 180°

  s +(4s) +(4s +s) = 180°

  10s = 180° . . . . . . . . . . . simplify

  s = 18° . . . . . . . . . divide by 10

  4s = 72° . . . . . . find the middle angle

  4s +s = 72° +18° = 90° . . . . . find the largest angle

The smallest, largest, and middle angles are 18°, 90°, and 72°, respectively.

Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.