Answer: " x = 110 " .
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180 – 140 = 40° . That is the angle of one side of the triangle given.
Note: The particular angle in the "unknown" angle in the triangle given, near the "140° angle", is supplementary to the "140° angle" ; and supplementary angles add up to "180° " .
180 – 110 = 70° . That is the angle of one side of the triangle given.
Note: This particular angle in the "unknown" angle in the triangle given, near the "110° angle", is supplementary to the "140° angle" ; and supplementary angles add up to "180° " .
We now know that 2 (TWO) of the measurements given in the triangle shown are: "40° " and "70° " .
Now, we shall find the measurement of the remaining angle in the triangle shown.
Note that in any triangle, all three (3) angles add up to "180° " .
So, to find the remaining angle in the triangle given {that is; the "angle nearest to "x"} ; we do so as follows:
180 – (40 + 70) = 180 – 110 = 70° .
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→ Now, since "x" is supplementary to this "70° " angle;
& since "supplementary angles" add up to " 180° " ;
→ x = 180 – 70 = 110° .
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→ x = 110 .
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OTHER METHOD:
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The given "110° angle (in the "image attached") and "x" are
"alternate exterior angles" ; and "alternate exterior angles are equal;
as such: " x = 110 " .
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