[tex]\begin{gathered} x\text{ = 9, y = 13} \\ m\angle W\text{ = m}\angle N\text{ = 91} \\ m\angle\text{ H = m}\angle O\text{ = 44} \\ m\angle Y\text{ = m}\angle T\text{ = 45} \end{gathered}[/tex]
Firstly, we want to start by drawing the triangles
We have this as follow;
For triangle HOT, we have;
We want to get the values of x and y firstly
Since both triangles are congruent, the order of the sides match
Hence, we have angle O and H equal
Thus, we have that;
[tex]\begin{gathered} 5x-1\text{ = 3x+ 17} \\ 5x-3x\text{ = 17+1} \\ 2x\text{ = 18} \\ x\text{ = }\frac{18}{2} \\ x\text{ = 9} \end{gathered}[/tex]
Now, to find Y, we need the measure of angle N
Angle N is same as W which we already have as 5y+ 26
Substitute N for Y
Since all the angles of a triangle sum up to 180, we have it that;
[tex]\begin{gathered} 5x-1\text{ + 4x + 9 + }(5y\text{ + 26) = 180} \\ 9x+8+5y+26\text{ = 180} \\ 9(9)\text{ + 5y + 34 = 180} \\ 5y\text{ = 180-34-81} \\ 5y\text{ = 65} \\ y\text{ = }\frac{65}{5} \\ y\text{ = 13} \end{gathered}[/tex]
Now, we want the measure of each of the angles;
1. W = N = 5y+ 26 = 5(13) + 26 = 91
2. H = O = 5x-1 = 5(9) - 1 = 44
3. Y = T = 4x + 9 = 4(9) + 9 = 45
