Here , we are going to use the property of linear pair . So , this property states that on any line , the sum of all angles formed by drawing other lines on the initial line is 180° or π radians .
__________________________
Coming back to the question , we are provided that ;
- [tex]{\sf \angle \: 1 = (x-18)^{\circ}}[/tex]
- [tex]{\sf \angle \: 2 = {5x}^{\circ}}[/tex]
Now by property of linear pair , we have ;
[tex]{: \implies \quad \sf \angle \: 1 + \angle \: 2 = 180^{\circ}}[/tex]
Putting the values ;
[tex]{: \implies \quad \sf x - 18^{\circ} + 5x = 180^{\circ}}[/tex]
[tex]{: \implies \quad \sf 6x = 180^{\circ}+18^{\circ}}[/tex]
[tex]{: \implies \quad \sf 6x=198^{\circ}}[/tex]
[tex]{: \implies \quad \sf x = \dfrac{198^{\circ}}{6}}[/tex]
[tex]{: \implies \quad \sf x=33^{\circ}}[/tex]
Now , we can find measures of [tex]{\sf \angle \: 1}[/tex] & [tex]{\sf \angle \: 2}[/tex] , by putting the value of x
[tex]{: \implies \quad \sf \angle \: 1 = (x-18)^{\circ}}[/tex]
[tex]{: \implies \quad \sf \angle \: 1 = (33-18)^{\circ}}[/tex]
[tex]{\boxed{\bf \therefore \quad \angle \: 1 = 15^{\circ}}}[/tex]
[tex]{: \implies \quad \sf \angle \: 2 = {5x}^{\circ}}[/tex]
[tex]{: \implies \quad \sf \angle \: 2 = {5\times 33}^{\circ}}[/tex]
[tex]{\boxed{\bf \therefore \quad \angle \: 2 = {165}^{\circ}}}[/tex]
We are Done :D
