In an isosceles triangle, line segment AC is congruent to line segment AB. Find the value of y in terms of x if one of the remote interior angle is y and the exterior angle is 3x+20.
I think the answer is y=6x-140 but I don't know how they got it.
Y is actually the vertex angle, as one of the remote interior angle.
If I read this ,
y and (3x+20) would be supplementary angles, that is they add up to 180°
y + 3x+20 = 180
y = 160-2x
However, your suggested answer is y = 6x-140, indicating that each of the equal angles could be 3x+20
in that case:
y + 2(3x+20) = 180
y + 6x + 40 = 180
y = 140 - 6x
To find the value of y in terms of x, we can start by considering the properties of isosceles triangles.
In an isosceles triangle, two sides are congruent. In this case, we are given that line segment AC is congruent to line segment AB.
Now let's focus on the exterior angle of the triangle. By definition, the exterior angle of a triangle is equal to the sum of the two remote interior angles.
Let's assign variables to the remote interior angles. We'll call the first remote interior angle y (as given in the problem) and the second remote interior angle z.
From the given information, we know that the exterior angle is 3x + 20. Therefore, we can set up an equation:
3x + 20 = y + z
Since we have an isosceles triangle, we can deduce that the two remote interior angles are congruent. Therefore, we can rewrite the equation as:
3x + 20 = y + y
3x + 20 = 2y
Now, we need to solve this equation for y in terms of x. Let's isolate y:
2y = 3x + 20
Divide both sides by 2:
y = (3x + 20) / 2
To simplify the expression further, we can distribute the division:
y = 3x/2 + 20/2
y = (3/2)x + 10
So, in terms of x, we found that the value of y is (3/2)x + 10.
Based on this explanation, it seems that the answer you provided, y = 6x - 140, is not correct. The correct expression for y in terms of x is y = (3/2)x + 10.