Question
Find d in the figure. (1 point)
on top of the triangle is the number 50degree on the bottom left is 70degree and on the right is a blank with a c inside the triangle and d outside
on top of the triangle is the number 50degree on the bottom left is 70degree and on the right is a blank with a c inside the triangle and d outside
Answers
GPT-4o mini
To find the angle \( d \) in the figure you've described, we can use the properties of a triangle.
In any triangle, the sum of the interior angles is always \( 180^\circ \). Given the angles of your triangle:
- One angle is \( 50^\circ \)
- Another angle is \( 70^\circ \)
Let's denote the third angle (the one with \( c \)) as \( c \). We can set up the equation:
\[
50^\circ + 70^\circ + c = 180^\circ
\]
Calculating this gives:
\[
120^\circ + c = 180^\circ
\]
Subtracting \( 120^\circ \) from both sides:
\[
c = 180^\circ - 120^\circ = 60^\circ
\]
Now, if the triangle is inside the figure and \( d \) is an exterior angle, then the exterior angle \( d \) is equal to the sum of the two opposite interior angles (which are \( 50^\circ \) and \( 70^\circ \)).
Thus,
\[
d = 50^\circ + 70^\circ = 120^\circ
\]
So \( d \) is \( 120^\circ \).
In any triangle, the sum of the interior angles is always \( 180^\circ \). Given the angles of your triangle:
- One angle is \( 50^\circ \)
- Another angle is \( 70^\circ \)
Let's denote the third angle (the one with \( c \)) as \( c \). We can set up the equation:
\[
50^\circ + 70^\circ + c = 180^\circ
\]
Calculating this gives:
\[
120^\circ + c = 180^\circ
\]
Subtracting \( 120^\circ \) from both sides:
\[
c = 180^\circ - 120^\circ = 60^\circ
\]
Now, if the triangle is inside the figure and \( d \) is an exterior angle, then the exterior angle \( d \) is equal to the sum of the two opposite interior angles (which are \( 50^\circ \) and \( 70^\circ \)).
Thus,
\[
d = 50^\circ + 70^\circ = 120^\circ
\]
So \( d \) is \( 120^\circ \).