Question

The measure of two angles of a quadrilateral are 75 and 105. Find the measure of each of remaining angles if measure of one angle is twice the other.

Answer 1

105+75+2x+x=360
182+2x=360
2x+x=360-182=178
x=59.3

Answer 2

The measure of remaining angles are 60 degrees and 120 degrees

Solution:

The sum of measure of all four angles in quadrilateral is 360 degrees

Given that,

The measure of two angles of a quadrilateral are 75 and 105

Let "x" be the measure of third angle

The measure of one angle is twice the other

Therefore, other angle is 2x

Therefore,

75 + 105 + x + 2x = 360

3x + 180 = 360

3x = 360 - 180

3x = 180

x = 60

Thus , 2x = 2(60) = 120

Thus the measure of remaining angles are 60 degrees and 120 degrees

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