the measure of two angles of a quadrilateral are 110° and 100° the remaining two angles are equal. Find the measure of each of the remaining two angles.
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Answers
Answer:
The angles of a quadrilateral add up to 360 degrees.
The first two angles (110 and 85) add up to 195 degrees.
If all four add up to 360, then the two remaining angles add up to 360 - 195 = 165 degrees.
We'll call our missing angles x and y.
We know that they add up to 165, so
x + y = 165
We also know that the ratio of the two angles is 14:19. We can also write this as 14/19, so x/y = 14/19.
It doesn't matter which order the x and y are in, because it doesn't matter which angle is x and which is y.
In this case, the smaller angle is x.
We now have two equations and two unknowns. Let's solve for x in the second equation by multiplying both sides by y. Now our two equations are:
x + y = 165
x = (14/19)*y
We can substitute (14/19)*y into our first equation for x:
(14/19)*y + y = 165
(33/19)* y = 165
Multiply both sides by 19/33 to get y=95
We can plug that into either equation to solve for x:
x + 95 = 165
x = 70
The two angles are 70 degrees and 95 degrees
Answer:
the two degrees angles are 70 degrees and 95 degrees