Question

In a quadrilatetral abcd ,the measure of the three angles a, b, and c are 110 , 70 and 80 , respectively .find the measure of the fourth angle

Answer 1

✨✨Answer is here✨✨

➡️✨✨see this pic✨✨

✔️✔️

Answer 2

Answer:

Step-by-step explanation:

Let the measure of the fourth angle be x°.  

We know that the sum of the angles of a quadrilateral is 360°.  

 

Therefore, 54 + 80 + 116 + x = 360  

⇒ 250 + x = 360

⇒ x = (360 - 250) = 110.

Hence, the measure of the fourth angle is 110°.

2. The three angles of the quadrilateral are 90°, 105°, 85°. Find the measure of the fourth angle of a quadrilateral.

Solution:

We know that sum of all the angles of a quadrilateral is 360°.

Let the unknown angle of the quadrilateral be x.

Then 90° + 105° + 85° + x = 360°

⇒ 280° + x = 360°  

⇒ x = 360 - 280

⇒ x = 80°

Therefore, the measure of the fourth angle of the quadrilateral is 80°

3. The measures of two angles of a quadrilateral are 115°and 45°, and the other two angles are equal. Find the measure of each of the equal angles.

Solution:

Let the measure of each of the equal angles be x°.

We know that the sum of all the angles of a quadrilateral is 360°.

Therefore, 115 + 45 + x + x = 360

⇒ 160 + 2x = 360

⇒ 2x = (360 - 160) = 200

⇒ x = 100.

Hence, the measure of each of the equal angles is 100