Question

simply this question ​

Answer 1

here's your answer

$\bf{\dag}\:{\underline{\underline{\sf{Question\::}}}}$

An angle of a quadrilateral measures five-third of a right angle and other three angles are equal. Find the measure of each of the equal angles.

$\bf{\dag}\:{\underline{\underline{\sf{Answer\::}}}}$

Each of the equal angles of quadrilateral measures 70°.

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━

$\bf{\dag}\:{\underline{\underline{\sf{Given\::}}}}$

One angle of quadrilateral = 5/3(Right angle)

Other three angles of quadrilateral are equal

$\bf{\dag}\:{\underline{\underline{\sf{To\:Find\::}}}}$

Measure of each equal angles?

$\bf{\dag}\:{\underline{\underline{\sf{Solution\::}}}}$

☯ We know that, one angle of quadrilateral is 5/3 of right angle it means one angle of quadrilateral is 5/3 of 90°. Therefore;

$\\ :\implies\:\tt One\:angle = \dfrac{5}{3}\:of\:90$

$\\ :\implies\:\tt One\:angle = \dfrac{5}{\cancel{3}}\:\times\:\cancel{90}$

$\\ :\implies\:\tt One\:angle = 5\:\times\:30$

$\\ :\implies\:{\underline{\boxed{\tt{One\:angle = 150^{\circ}}}}}$

☯ Hence, one angle of quadrilateral measures 150° and we know that other three angles are equal.

Let each equal angle be y

We know that,

$\quad\bigstar\:{\boxed{\sf{\pink{Sum_{(angles\:of\:quadrilateral)} = 360^{\circ}}}}}$

Therefore,

$\\ :\implies\:\tt 150 + y + y + y = 360$

$\\ :\implies\:\tt 150 + 3y = 360$

$\\ :\implies\:\tt 3y + 150 = 360$

$\\ :\implies\:\tt 3y = 360 - 150$

$\\ :\implies\:\tt 3y = 360 - 150$

$\\ :\implies\:\tt 3y = 210$

$\\ :\implies\:\tt y = {\cancel{\dfrac{210}{3}}}$

$\\ :\implies\:{\underline{\boxed{\tt{y = 70^{\circ}}}}}$

Hence, each of the equal angles of quadrilateral measures 70°.

Related Question:

In the given figuree, AB||CD, ∠EAB = 50° and ∠ECD = 60°, then find ∠AEB.

Answer:

brainly.in/question/46043317

Know more:

Sum of angles of any quadrilateral is 360° and sum of angles of any triangle is 180°.

▬▬▬▬▬▬▬▬▬▬▬▬