Question

. Three angles of a quadrilateral are equal and the measure of 4" angle is 120°. Find the measure of each of the equal angles.​

Answer 1

Given: Three angles of a quadrilateral are equal and the measure of fourth angle is 120°.

Need to Find: The measure of each of the equal angle?

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❍ Let's say the equal angle of the quadrilateral be x.

As we know that,

❝Sum of all angles of a quadrilateral is 360°.❞

Therefore:

$\qquad\star\; \underline{\boxed{\pmb{\sf{Sum\; of\; angles\; of\; Quadrilateral={360}^{\circ}}}}}$

where,

• Fourth angle of Quadrilateral is given, that is 120°

⠀

$\underline{\dagger\; \frak{Substituting\; the\; values\; :}}$

$\\\\:\implies\quad\sf{x+x+x+{120}^{\circ}={360}^{\circ}}$

$\\\\:\implies\quad\sf{3x+{120}^{\circ}={360}^{\circ}}$

$\\\\:\implies\quad\sf{3x={360}^{\circ}-{120}^{\circ}}$

$\\\\:\implies\quad\sf{3x={240}^{\circ}}$

$\\\\:\implies\quad\sf{x=\cancel{\dfrac{{240}^{\circ}}{3}}}$

$\\\\:\implies\quad\underline{\boxed{\pmb{\frak{\purple{x={80}^{\circ}}}}}}\;\bigstar$

⠀

$\sf{\therefore\;\underline{Hence,\; the\; measure\; of\; equal\; angles\; is\; \pmb{{80}^{\circ}}}}$

Answer 2

Answer:

Measure of each angle = 80°

Step-by-step explanation:

$\pink{\huge{\dagger}}\bold{\underline{Given:-}}$

❒ Three angles of a quadrilateral are equal

❒ "Fourth" angle measures = 120°

$\red{\huge{\dagger}}\bold{\underline{To\:Find:-}}$

☞ Find the measure of each of the equal angles.​

$\red{\huge{\dagger}}\bold{\underline{Solution:-}}$

It is given that three angles are equal and measure of fourth angle is 120°

Let the measure of each of the equal angles be $x$

We know that, sum of four measure of angle 180°

$\Rightarrow x+x+x+120^o = 360^o$

$\Rightarrow 3x+120^o = 360^o$

$\Rightarrow 3x = 340^o-120^o$

$\Rightarrow 3x = 240^o$

$\Rightarrow x = \frac{240}{3}$

$\Rightarrow x = 80^o$

$\bigstar$ Measure of each angle = 80°$\bigstar$