Question

In 4-6 sentences explain how to find the measure of each angle indicated.

m<M
top left corner K
bottom left corner N
Right top corner L
Right bottom corner M
inside left top corner 80
inside left bottom corner 9x-1
inside top right corner 9x-5
inside bottom right corner 16+9x

Answer 1

To find the measure of angle \( M \), we can set up an equation using the property that the sum of the angles in a quadrilateral equals 360 degrees. In this case, we have four angles, with measures \( 80^\circ \), \( 9x - 1 \), \( 9x - 5 \), and \( 16 + 9x \).

We can write the equation:

\[
80 + (9x - 1) + (9x - 5) + (16 + 9x) = 360
\]

Next, simplify the equation by combining like terms. This yields:

\[
80 - 1 - 5 + 16 + 27x = 360
\]

\[
90 + 27x = 360
\]

Finally, isolate \( x \) by subtracting 90 from both sides and then dividing by 27:

\[
27x = 270
\]

\[
x = 10
\]

Now, substitute \( x \) back into each angle expression to find their measures, including angle \( M \).