A side of the triangle below has been extended to form an exterior angle of 160°. Find the value of x.
Left: 160. Right: 48.
Since the sum of the exterior angles of a triangle is always 360°, and the right angle is 90°, the remaining angle in the triangle is 360° - 160° - 90° = 110°.
Since the triangle is isosceles (because the left and right angles are congruent), the remaining two sides must be congruent.
Therefore, the value of x is 110°/2 = <<110/2=55>>55°. Answer: \boxed{55}.
wrong.
I apologize for the mistake. Let's try again.
Since the exterior angle on the left side is 160° and the interior angles of a triangle sum to 180°, the corresponding interior angle is 180° - 160° = 20°.
Since the triangle is isosceles (the left and right angles are congruent), the remaining two interior angles are also congruent.
Let's call the value of each of these congruent angles x.
Since the sum of the angles in a triangle is 180°, we can write the equation:
x + x + 20° + 90° = 180°
Combining like terms, we get:
2x + 110° = 180°
Subtracting 110° from both sides, we have:
2x = 70°
Dividing both sides by 2, we get:
x = 35°
Therefore, the value of x is 35°. Answer: \boxed{35}.
To find the value of x, we need to use the property that the exterior angle of a triangle is equal to the sum of its interior opposite angles.
In this case, we have an exterior angle of 160°, so we can set up the equation:
x + 48° = 160°
To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting 48° from both sides:
x + 48° - 48° = 160° - 48°
Simplifying further, we have:
x = 160° - 48°
Calculating this, we get:
x = 112°
Therefore, the value of x is 112°.