Question

Three angles of a triangle are 2x + 4°.
3.x-5° and x+13°. Write an equation in
r and hence find its angles. Calculate the
measure of its exterior angles. What is the
total of the three exterior angles?​

Answer 1

Step-by-step explanation:

Three angles of triangles are 2x +4°, 3x + 5° and x + 13°

Sum of interior angles of triangle is 180°

So,

2x +4° +3x - 5° + x + 13° = 180°

6x + 12° = 180°

6x = 180° - 12° = 168°

x = 168°/6 = 28°

Angles are

2*28+4 = 60°

3*28-5 = 79°

28+13 = 41°

Refer the attached figure

To find exterior angles

Exterior angle is sum of opposite 2 angles

$E_a = 79 + 41 = 120 \\ E_b = 60 + 41 = 101 \\ E_c = 60 + 79 = 139$

Sum of exterior angles of triangle is 360°

$E_a + E_b + E_c = 120 + 101 + 139 = 360$