Question

An angle of a quadrilateral is 120 degree the other three angles are equal find the measure of each of the angles. ​

Answer 1

$\huge{\pink{\green {\sf\boxed{ANSWER}}}}$

$\small\boxed{\angle B = 80°,\angle C = 80°,\angle D = 80°}$

$\huge{\pink {\sf\underline{Step\: by\: step\: explanation ⟹}}}$

Let angles ∠B, ∠C, ∠D are$</strong><strong>\</strong><strong>:</strong><strong>{</strong><strong>x</strong><strong>°</strong><strong>}$

Sum of all angles of a quadrilateral is = ${</strong><strong>360</strong><strong>°</strong><strong>}$

∴ ∠A + ∠B + ∠C + ∠D = 360°

$</strong><strong>⟹</strong><strong> {</strong><strong>120</strong><strong>°</strong><strong>+</strong><strong> </strong><strong>x</strong><strong>°</strong><strong>+</strong><strong> </strong><strong>x</strong><strong>°</strong><strong>+</strong><strong> </strong><strong>x</strong><strong>°</strong><strong> </strong><strong>=</strong><strong> </strong><strong>360</strong><strong>°</strong><strong>}$ [∠A=120°]given

$⟹ {120°+ 3x° = 360°}$

$⟹ {3x° = 360° - 120°}$

$</strong><strong>⟹</strong><strong>{</strong><strong>3x°</strong><strong>}</strong><strong> = </strong><strong>{</strong><strong>240</strong><strong>°}$

$⟹</strong><strong> </strong><strong>{</strong><strong>x° </strong><strong>=\d</strong><strong>frac</strong><strong> </strong><strong>{</strong><strong>240</strong><strong>°</strong><strong>}</strong><strong>{</strong><strong>3</strong><strong>°</strong><strong>}</strong><strong>}</strong><strong> </strong><strong>$

$⟹</strong><strong> </strong><strong>{</strong><strong>x° = </strong><strong>80</strong><strong>°</strong><strong>}$

$\bold {\pink{\green {\sf\underline{ ∴\angle B = x°={\boxed {80°}}}}}}$

$\bold {\pink{\green {\sf\</strong><strong>underline</strong><strong>{</strong><strong> \angle </strong><strong>C</strong><strong> = x°={\boxed {80°}}}}}}$

$\bold {\pink{\green {\sf\underline{ \angle </strong><strong>D</strong><strong> = x°={\boxed {80°}}}}}}$

$\Large\boxed{</strong><strong>Solved</strong><strong>}$

#Be_Brainly

Answer 2

Answer:

Step-by-step explanation:

Triangle = sum of all side is equal to 180

One side is 120

Sum of Two sides = 180 - 120

= 60

Therefore, one side = 60 ÷ 2

= 30

The remaining side will be also 30 degree

One side = 120

Second side = 30

Third side = 30