Find d

Question

d
in the figure. (1 point)
An illustration shows a triangle with a left angle of 70 degrees and a top angle of 50 degrees. The angle at the right is labeled c. A horizontal line extending outward from c forms an exterior angle that is labeled d.

Answer 1

To find the value of angle \( d \) in the triangle described, we start by finding the missing angle \( c \) in the triangle.

In a triangle, the sum of all interior angles is always \( 180^\circ \). Given that one angle is \( 70^\circ \) and another angle is \( 50^\circ \), we can find angle \( c \) using the following calculation:

\[ c = 180^\circ - (70^\circ + 50^\circ) \]

Calculating the sum of the known angles:

\[ 70^\circ + 50^\circ = 120^\circ \]

Now, substituting this into the equation for \( c \):

\[ c = 180^\circ - 120^\circ = 60^\circ \]

Now we know that angle \( c \) measures \( 60^\circ \).

Next, we can find the exterior angle \( d \). The exterior angle \( d \) at vertex \( c \) is equal to the sum of the two opposite interior angles (angles \( 70^\circ \) and \( 50^\circ \)). Thus, we can compute \( d \):

\[ d = 70^\circ + 50^\circ = 120^\circ \]

So, the value of angle \( d \) is

\[ \boxed{120^\circ} \]