Question

Three angles of a quadrilateral are equal. If the fourth angle is 105°, find the magnitude of each of the equal angles.​

Answer 1

Step-by-step explanation:

Three angles of a quadrilateral are equal and the measure of the fourth angle is 120o. Find the measure of each of the equal angles.

Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM

Expert Answer:

Let x be one the three equal angles.

Sum of all the angles of a quadrilateral = 360o

⇒ x + x + x + 120o = 360o

⇒ 3x = 360o -120o

⇒ 3x = 240o

⇒ x = 80o

Thus, the measure of each of the equal angle is 80o.

Answer 2

☆ Solution ☆

Given :-

• Three angles of a quadrilateral are equal.
• The fourth angle of a quardilateral is 105°.

To Find :-

• The magnitude of each of the equal angles.

Step-by-Step-Explaination :-

Let,

• The equal angles of the quadrilateral be x

Now,

As we know that :-

Sum of all angles of a quadrilateral = 360°

According to the question :-

x + x + x + 105° = 360°

3x + 105° = 360°

3x = 360° - 105°

3x = 255° x = 255/3

x = 85°

Hence,

The measures of three angles are 85°. _____________________________

Verification :-

As we know that :-

Sum of all angles of a quadrilateral = 360°

According to the question :-

85° + 85° + 85° + 105° = 360°

360° = 360°

Hence Verified !_____________________________