A side of the triangle below has been extended to form an exterior angle of 134°. Find the value of xx.
Let the side of the triangle that has been extended be AB, with the exterior angle formed at point B. Let the point at which the extension intersects the line containing side AC be D. Let the point at which the extension intersects the line containing side BC be E. Since the sum of the angles of a triangle is 180°, we know that ∠BAC + ∠ABC + ∠ACB = 180°.
Let x be the measure of ∠BAC. Since ABC is a right triangle, we know that ∠ABC = 90°. We can now rewrite our equation as x + 90° + ∠ACB = 180°.
Since exterior angles of a triangle sum to 360°, we know that ∠ACB + ∠BCE = 360°. Therefore, ∠ACB + 134° = 360°.
Simplifying this equation, we find ∠ACB = 360° - 134° = 226°.
Now we can substitute this value back into our original equation to find x: x + 90° + 226° = 180°.
Simplifying this equation, we find x = 180° - 90° - 226° = -136°.
Since angles cannot be negative, we can conclude that there is no valid value for x that satisfies the conditions of the problem.
try again.
Apologies for the mistake. Let's try again.
Since the exterior angle is formed by extending one side of the triangle, we can state that the exterior angle is equal to the sum of the two opposite interior angles.
Let x be the measure of the exterior angle. Let's call the interior angles at points A and C y and z, respectively.
Therefore, we have x = y + z.
Since the sum of the angles of a triangle is 180 degrees, we have y + z + x = 180.
Substituting x = 134, we get y + z + 134 = 180.
Rearranging the equation, we have y + z = 180 - 134 = 46.
Let's label the exterior point as D, where D is on the extension of side AB.
Now, in triangle ACD, the sum of the interior angles is 180 degrees. So, we have y + 134 + z = 180.
Substituting y + z = 46, we get 46 + 134 = 180.
Therefore, we find that the angles at A and C are 46 degrees each.
Since the triangle is isosceles (having two equal angles at A and C), the remaining angle at B is 180 - 2 * 46 = 180 - 92 = 88 degrees.
Thus, we have found all the angles of the triangle, and we can conclude that the value of x is equal to 134 degrees.
To find the value of xx, we need to use the fact that the sum of the measures of the interior angles of a triangle is always 180 degrees.
In this case, the exterior angle of the triangle is given to be 134 degrees. An exterior angle is formed by extending one side of the triangle. So, we can find the measure of the corresponding interior angle by subtracting the exterior angle from 180 degrees.
Let's call the interior angle corresponding to the given exterior angle "y".
y = 180° - 134°
y = 46°
Now, let's examine the triangle to find the value of xx. Since the angle opposite to the extended side is equal to the interior angle y, we can find the value of xx by subtracting y from 180 degrees.
x + y + xx = 180°
xx = 180° - y
xx = 180° - 46°
xx = 134°
Therefore, the value of xx is 134 degrees.