Use the image to answer the question.

Question

An illustration shows a rectangle which is segmented left to right into a right triangle, a trapezoid in the middle, and another right triangle. The sides of the rectangle form the sides of the triangles. The top corners of the rectangle are denoted by two right angle symbols. The middle trapezoid is formed by two slanting lines from each of the top corners to the base of the rectangle. The angles formed by the two slanted lines, which become the hypotenuse of each right triangle, are labeled from 1 to 8 in clockwise direction starting from the top of the left side.

If m∠8=45°
, what equation can you write to find the value of m∠7
?

(1 point)
m∠7+
°=
°

Answer 1

Given that \( m\angle 8 = 45^\circ \), we can analyze the relationship between the angles in the trapezoid and triangles.

Since angles \( \angle 7 \) and \( \angle 8 \) are adjacent angles on a straight line (the top line of the trapezoid), they are supplementary. Therefore, we can write the equation:

\[ m\angle 7 + m\angle 8 = 180^\circ \]

Substituting the given value for \( m\angle 8 \):

\[ m\angle 7 + 45^\circ = 180^\circ \]

Thus, to find the equation you are looking for:

\[ m\angle 7 + 45^\circ = 180^\circ \]