9. AC ATis an isosceles triangle with base angles Cand Teach represented by (3 x +11) degrees, while angle A is represented by (9 x+8) degrees. Find the measure of angle

C.

41°

Step-by-step explanation:

A triangle is a shape with three angles and three sides. There are different types of triangles such as equilateral triangle, scalene triangle, isosceles triangle, right angled triangle and so on.

An isosceles triangle is a triangle in which two sides and two angles are equal to each other.

In triangle CAT, ∠C = ∠T (base angles of an isosceles triangle are equal):

∠A + ∠C + ∠T = 180° (sum of angles in a triangle).

Hence substituting gives::

(9x + 8) + (3x + 11) + (3x + 11) = 180

9x + 3x + 3x + 8 + 11 + 11 = 180

15x + 30 = 180

15x = 180 - 30

15x = 150

x = 150 / 15

x = 10°

Hence ∠A = 9x + 8 = 9(10) + 8 = 98°, ∠C = ∠T = 3x + 11 = 3(10) + 11 = 30 + 11 = 41°