A side of the triangle below has been extended to form an exterior angle of 136°. Find the value of x.
Left: 136. Right: x.
The sum of the measures of the exterior angles of a triangle is always 360 degrees. Since one of the exterior angles is given as 136 degrees and the other two angles of the triangle are 136 and x degrees, we can set up the equation:
136 + 136 + x = 360
Combine like terms:
272 + x = 360
Subtract 272 from both sides:
x = 360 - 272
x = 88
Therefore, the value of x is 88.
wrong.
Apologies for the mistake. Let's approach the problem correctly.
Since the given angle is an exterior angle of the triangle, it is equal to the sum of the two remote interior angles. In other words, 136° + x° = 180°.
To find the value of x, we can solve this equation by subtracting 136° from both sides:
x° = 180° - 136°
x° = 44°
Therefore, the value of x is 44.
To find the value of x in the given triangle, we need to use the property that the sum of the exterior angles of any triangle is always equal to 360 degrees.
In this case, the given exterior angle is 136 degrees. So, the sum of the other two interior angles must be equal to 360 - 136 = 224 degrees.
Since both the left and right interior angles are supplementary to the given exterior angle, we can write the following equation:
Left + Right = 224 degrees
We are given the measure of the left interior angle as 136 degrees. Plugging this into the equation, we get:
136 + Right = 224
To solve for Right, we need to isolate it on one side of the equation. Subtracting 136 from both sides, we have:
Right = 224 - 136
Right = 88
Therefore, the value of x (which represents the measure of the right interior angle) is 88 degrees.