Question

6. The measures of external angles of a quadrilateral are (2x - 15), (x + 45), (3x )°
and (2x + 10). What is the measure of the smallest angle of the quadrilateral?
(1) 65°
(2) 60° (3) 85° (4) 55°​

Answer 1

Answer:

65°

Step-by-step explanation:

Sum of all exterior angles of a quadrilateral or any polygon is always 360°

Hence,

(2x - 15) + (x + 45) + (3x ) + (2x + 10) = 360°

2x - 15 + x + 45 + 3x + 2x + 10 = 360°

8x + 40° = 360°

x = (360° - 40°) /8 = 40°

Now, find all the exterior angle

Value of the first angle =(2x-15)=[2(40) -15] = 65°

Value of the second angle =(x+45)= 40 + 45 = 85°

Value of the third angle = 3x = 3(40) = 120°

Value of the fourh angle =(2x+10)=[2(40) +10] = 90°

By comparing smallest angle is 65°