Question

23. ABCD is a rectangle. If m21-5x and m22 - 8x -1, find x, m<1, and m<2.ABEDm

Answer 1

If ABCD is a rectangle, each of its four angles at the vertex is a right angle.

Then the angle at D is a right angle (measure of 90 degrees).

The right angle is divided in two angles, <1 and <2, by the diagonal, so <1 and <2 are complementary.

Then, we can write:

`\begin{gathered} m\angle D=m\angle1+m\angle2=90\degree \\ (5x)+(8x-1)=90 \\ 13x-1=90 \\ 13x=90+1 \\ 13x=91 \\ x=(91)/(13) \\ x=7 \end{gathered}`

Then, with the value of x we can calculate m<1 and m<2:

`\begin{gathered} m\angle1=5x=5\cdot7=35\degree \\ m\angle2=8x-1=8\cdot7-1=56-1=55\degree \end{gathered}`

Answer:

x = 7

m<1 = 35º

m<2 = 55º