Question

Question

Use the image to answer the 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

To find the value of \( m∠7 \), we can use the fact that angles on a straight line sum to \( 180^\circ \).

In this case, angles \( m∠7 \) and \( m∠8 \) are adjacent angles that form a linear pair (they are supplementary). Therefore, we can set up the equation:

\[ m∠7 + m∠8 = 180^\circ \]

Given that \( m∠8 = 45^\circ \), we can substitute that into the equation:

\[ m∠7 + 45^\circ = 180^\circ \]

Thus, the equation that can be written to find the value of \( m∠7 \) is:

\[ m∠7 + 45^\circ = 180^\circ \]