20095212idn
Answered

Connect with a community that values knowledge and expertise on IDNLearn.com. Our experts provide accurate and detailed responses to help you navigate any topic or issue with confidence.

_____________________

The sizes of the interior angles of a triangle are in the ratio 1:3:8 Calculate the difference in size between the largest and smallest angles.

Please answer me!

_____________________

Sagot :

KimYuriiidn

Answer:

105°

Step-by-step explanation:

We have,

  • The inferior angles of the triangle are in the ratio 1:3:8.

We've to calculate the difference in size between the largest and smallest angles.

Let's find the sizes or the values of the angles first.

Let us assume the interior angles of triangle as 1x , 3x and 8x as they are in the ratio 1:3:8.

★ According to the angle sum property of the triangle, the sum of the interior angles of the triangle is 180°. So,

→ 1x + 3x + 8x = 180°

→ 12x = 180°

→ x = 180° ÷ 12

→ x = 15°

Now, the sizes of the angles are,

  • First angle = 1x = 1(15) = 15°
  • Second angle = 3x = 3(15) = 45°
  • Third angle = 8x = 8(15) = 120°

First angle is the smallest angle and the third one is the largest.

→ Difference = Third angle – First angle

→ Difference = 120° – 15°

→ Difference = 105°

Therefore, the difference in size between the largest and smallest angle is 105°.

We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Thank you for trusting IDNLearn.com. We’re dedicated to providing accurate answers, so visit us again for more solutions.