A side of the triangle below has been extended to form an exterior angle of 136°. Find the value of x.
To find the value of x, we need to use the fact that the sum of an exterior angle and its corresponding interior angle is 180°.
Let x be the measure of the interior angle of the triangle.
Since the exterior angle has a measure of 136°, the corresponding interior angle has a measure of 180° - 136° = 44°.
Since the exterior angle and the corresponding interior angle have the extended side as a common side, the other two interior angles of the triangle must add up to 180° - 44° = 136°.
Therefore, the two interior angles opposite the extended side must each have a measure of 136°/2 = 68°.
Since the sum of the three interior angles of a triangle is 180°, we can write the equation:
x + 44° + 68° = 180°
Combining like terms, we have:
x + 112° = 180°
Subtracting 112° from both sides, we find:
x = 180° - 112° = 68°.
Therefore, the value of x is 68°.
thats not right bot
Apologies for the mistake. Let's approach the problem again.
In a triangle, each interior angle and its corresponding exterior angle add up to 180°. Since the exterior angle formed is 136°, the corresponding interior angle is 180° - 136° = 44°.
Let's call one of the interior angles of the triangle x°.
Since the sum of the interior angles of a triangle is 180°, the other two interior angles can be expressed as (180° - x°) and (44°).
To find x°, we add up the three interior angles and set it equal to 180°:
x° + (180° - x°) + 44° = 180°
Simplifying the equation, we get:
224° - x° = 180°
Rearranging the equation, we find:
x° = 224° - 180°
x° = 44°
Therefore, the value of x is 44°.
To find the value of x, we need to use the concept of exterior angles in a triangle.
The sum of the measures of the exterior angles of a triangle is always 360°.
In this case, the exterior angle formed is 136°.
To find the value of x, we need to subtract the exterior angle from 360° and then divide the result by 2.
Let's set up the equation:
360° - 136° = 2x
Simplifying the equation:
224° = 2x
Now, divide both sides of the equation by 2:
x = 224° / 2
x = 112°