Question

14.The measures of two angles of a quadrilateral are 80 degrees and 120 degrees.If the remaining two angles are equal, the measure of each of the remaining two angles is _________
(1 Point)​

Answer 1

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°.

Answer 2

Step-by-step explanation:

let the measure of each remaining angles be x.

80 + 120 + x + x = 360

200 + 2x = 360

2x = 360 - 200

2x = 160

x = 160/2

x = 80

so the measure of remaining 2 angles is 80 degree each