In an isosceles triangle, the vertical angle measures angles of the triangle 3 1 7 times the base angle. Find the measure of all the angles of the triangle.

Given, Let the missing angles be x , x + x + 3 1 7 x = 180 o (Sum of the angles at point) ⇒ x + x + 22 7 x = 180 o ⇒ x + x + 22 x 7 = 180 o ⇒ 36 x = 180 o × 7 ⇒ 36 x = 1260 o ⇒ x = 1260 o 36 ⇒ x = 35 o Finding all the missing angles, x 1 = 35 o , x 2 = 35 o , x 3 = 22 7 × 35 o = 110 o Hence, the required answer is obtained.

In an isosceles triangle, the vertical angle measures angles of the triangle 3 1 7 times the base angle. Find the measure of all the angles of the triangle.

Given, Let the missing angles be x , x + x + 3 1 7 x = 180 o (Sum of the angles at point) ⇒ x + x + 22 7 x = 180 o ⇒ x + x + 22 x 7 = 180 o ⇒ 36 x = 180 o × 7 ⇒ 36 x = 1260 o ⇒ x = 1260 o 36 ⇒ x = 35 o Finding all the missing angles, x 1 = 35 o , x 2 = 35 o , x 3 = 22 7 × 35 o = 110 o Hence, the required answer is obtained.

In a right-angled triangle, one acute angle is 2 5 of the other. Find the measures of the two acute angles of the triangle.

Consider one of the acute angle of the right-angled triangle as x . Now, according to the given question the two acute angles are x , 2 5 x . Sum of the measures of three interior angles of a triangle is 180 ° . A right-angled triangle has only one right angle. So, the sum of the two acute angles of a right-angled triangle is 90 ° . i.e., x + 2 5 x = 90 ° ⇒ 7 x = 5 × 90 ° ⇒ x = 450 7 ° , 2 5 x = 450 7 × 2 5 = 180 7 ° Therefore, the required acute angles of the right-angled triangle are 450 7 ° and 180 7 ° .