Question

The interior angles of a hexagon are (2x+17)⁰, (3x -25)⁰,(2x+49)⁰, (x+40)⁰, (4x-17)⁰and (3x -4)⁰. i.Find the value of x. ii.Find the smallest interior angle of the hexagon. iii.Find the largest exterior angle of the hexagon. iv.Find the largest exterior angle of the hexagon. PLEASE PLEASE ANSWER MY QUESTION..I WILL THANK YOU AND ALSO MARK YOUR ANSWER AS BRAINLIEST ..KINDLY GIVE ME CORRECT ANSWER ASAP

Answer 1

(i) It is known that the sum of the interior angles of a hexagon is 720°.

According to the question,

2x°+17°+3x°-25°+2x°+49°+x°+40°+4x°-17°+3x°-4°=720°

=>15x°+60°=720°

=>15(x°+4°)= 15°×48°

=>x°+4°=48°

=>x°=48°-4°=44°

Thus, value of x=44°

The 6 angles are:-

2x°+17°=2(44)°+17°=88°+17°=105°

3x°-25°=3(44)°-25°=132°-25°=107°

2x°+49°=2(44)°+49°=88°+49°=137°

x°+40°=44°+40°=84°

4x°-17°=4(44)°+40°=176°+40°=216°

3x°-4°=3(44)°-4°=132°-4°=128°

(ii) Smallest interior angle = 84°

(iii) Largest exterior angle = Supplement of smallest interior angle =180°-84°=96°

(iv) same as (iii)

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