Question

If the angles of a triangle are arranged in the ascending order of their magnitudes and the difference between the two consecutive angles is 𝟏𝟎°, find the measure of all the three angles.​

Answer 1

Given that the angles are arranged in ascending order of their magnitude,
Let’s say that the angles of the triangles arranged in ascending order are x, (x+10), (x+20)
Sum of all the angles = (x) <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> °+ (x+10) <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ° + (x +20) <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ° = 180 <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> °
(3x) <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ° + 30 <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ° = 180 <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> °
(3x) <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ° = 180 <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ° - 30 <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> °
(3x) <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ° = 150 <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> °
x = 50 <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> °
x + 10 = 50 + 10 = 60 <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> °
x + 20 = 50 +20 = 70 <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> °
Therefore, the angles of the triangle are 50 <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> °, 60 <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> °, & 70 <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> °