Question
In isosceles triangle RST below, what is the value of y?
Triangle R S T. Angle T is 38 degrees and angles R and S are y.
38 degrees
71 degrees
122 degrees
142 degrees
Triangle R S T. Angle T is 38 degrees and angles R and S are y.
38 degrees
71 degrees
122 degrees
142 degrees
Answers
GPT-4o mini
In an isosceles triangle, the two angles that are equal are typically the base angles. In triangle RST, angles R and S are equal and both are denoted as \( y \). Angle T is given as \( 38^\circ \).
The sum of the angles in any triangle is always \( 180^\circ \). Therefore, we can set up the equation:
\[
y + y + 38^\circ = 180^\circ
\]
This simplifies to:
\[
2y + 38^\circ = 180^\circ
\]
Next, subtract \( 38^\circ \) from both sides:
\[
2y = 180^\circ - 38^\circ
\]
\[
2y = 142^\circ
\]
Now, divide both sides by 2:
\[
y = \frac{142^\circ}{2} = 71^\circ
\]
Thus, the value of \( y \) is \( 71^\circ \).
The correct answer is \( 71^\circ \).
The sum of the angles in any triangle is always \( 180^\circ \). Therefore, we can set up the equation:
\[
y + y + 38^\circ = 180^\circ
\]
This simplifies to:
\[
2y + 38^\circ = 180^\circ
\]
Next, subtract \( 38^\circ \) from both sides:
\[
2y = 180^\circ - 38^\circ
\]
\[
2y = 142^\circ
\]
Now, divide both sides by 2:
\[
y = \frac{142^\circ}{2} = 71^\circ
\]
Thus, the value of \( y \) is \( 71^\circ \).
The correct answer is \( 71^\circ \).