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°.
