two adjacent angles of a quadrilateral measure 130° and 40°. Then find the sum of the remaining two angles
Answers
Answer:
190°
Explanation:
Let ∠1 be 130° and ∠2 be 40°
Sum of all interior angles of a quadrilateral = 360°
So, ∠1 + ∠2 + ∠3 + ∠4 = 360°
130° + 40° + ∠3 + ∠4 = 360°
170° + ∠3 + ∠4 = 360°
∠3 + ∠4 = 360° - 170°
∠3 + ∠4 = 190°
Given:
The measure of 1st angle of two adjacent angles in the quadrilateral = 130°
The measure of 2nd angle of two adjacent angles in the quadrilateral = 40°
To find:
Sum of other two angles of quadrilateral =?
Solution:
A quadrilateral is a polygon having four sides and two of them are parallel to each other.
Two adjacent angles of a quadrilateral are those that share one common side.
To find sum total of the other two angles steps are:
=> Let "∠a" be the angle of one side.
=> Let "∠b" be the angle of another remaining side.
=> Let "Y" be the sum of two angles in this quadrilateral.
∴ Y = ∠a + ∠b
We know quadrilateral is the polygon in which angle of all the sides sums up to 360°.
∴ ∠1st adjacent angle + ∠2nd adjacent angle + ∠a +∠b = 360°
=> 130° + 40° + Y =360°
=> 170° + Y = 360°
=> Y = 360° - 170°
=> Y = 190°
=> ∠a + ∠b = 190°
Hence the sum of two remaining angles of a quadrilateral is 190°.