Question

Triangle Proofs Practice
Complete this assessment to review what you’ve learned. It will not count toward your grade.
2 of 52 of 5 Items


Question
Use the image to answer the question.

A quadrilateral is formed by joining four lines. The top left vertex is given as a 115 degrees, the top right vertex is given as b 120 degrees, the bottom right vertex is given as c 75 degrees, and the bottom left vertex is given as d 50 degrees.

Using the given angles, what is the interior angle measure of a?

(1 point)
interior angle a=
°

Answer 1

To find the interior angle \(a\) of the quadrilateral formed by the four angles (given as \(a = 115^\circ\), \(b = 120^\circ\), \(c = 75^\circ\), and \(d = 50^\circ\)), we first need to recall that the sum of the interior angles of a quadrilateral is always \(360^\circ\).

Given that we need to find \(a\) and we already have values for \(b\), \(c\), and \(d\):

\[
b + c + d = 120^\circ + 75^\circ + 50^\circ
\]

Calculating this gives:

\[
b + c + d = 120 + 75 + 50 = 245^\circ
\]

Now, we can find angle \(a\) by using the formula for the sum of the interior angles of a quadrilateral:

\[
a + b + c + d = 360^\circ
\]

Substituting the known values into the equation:

\[
a + 245^\circ = 360^\circ
\]

To isolate \(a\), subtract \(245^\circ\) from both sides:

\[
a = 360^\circ - 245^\circ
\]
\[
a = 115^\circ
\]

So, the interior angle measure of \(a\) is:

\[
\text{interior angle a} = 115^\circ
\]