Question

Given ABCD is a rectangle,

Answer 1

The equation to get z is;

(2z+15) + (2z-5) = 90

The measure of angle ABD is 55

Here, we want to calculate the measure of z

Mathematically, the angles at the edge of the rectangle measures 90 degrees

Thus, triangle ABD is a right-angled triangle

Thus;

$\begin{gathered} (2z+15)\text{ + (2z-5) + 90 = 180} \\ \\ (2z+15)\text{ + (2z-5) = 90} \\ 4z+10\text{ = 90} \\ \\ 4z\text{ = 90-10} \\ \\ 4z\text{ = 80} \\ \\ z\text{ = }\frac{80}{4} \\ \\ z\text{ = 20} \end{gathered}$

From the diagram, the angle ABD is the angle marked 2z+15

So let us substitute z for 20

We have;

2(20) + 15 = 40 + 15 = 55