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.​

Answer 1

Answer:

• 70° is the measure of each equal angles.

Step-by-step explanation:

According to the Question :

Let the three equal angles be x .

and , the fourth angle is 5/3 of right angle

→ fourth angle should be = 5/3 × 90° (as per given questions)

→ fourth angle = 5×30°

→ fourth angle = 150°

As we know that sum of all angles in a quadrilateral is 360°

So, by putting the values we get

➻ 150° + x + x + x = 360°

➻ 150° + 3x = 360°

➻ 3x = 360° - 150°

➻ 3x = 210°

➻ x = 210/3

➻ x = 70°

• Hence, the measure of each equal angles will be 70° respectively.

Answer 2

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

• 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°.

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

• 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°.

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