Q:

can someone help me with this question please!!!!!

Accepted Solution

A:
Solution:We know that:Interior angles of a triangle sum up to 180°.[tex]3a + 7u + 9 = 180\°[/tex]This means that:[tex](7u + 9) + (2a - 3) + 32 = 3a + 7u + 9[/tex]Let's simplify the equation to find a.Step-by step calculations:Open the brackets:[tex](7u + 9) + (2a - 3) + 32 = 3a + 7u + 9[/tex][tex]7u + 9 + 2a - 3 + 32 = 3a + 7u + 9[/tex]Cancel same terms on both sides:[tex]7u + 9 + 2a - 3 + 32 = 3a + 7u + 9[/tex][tex]2a - 3 + 32 = 3a[/tex]Simplify the LHS:[tex]2a + 29 = 3a[/tex]Subtract 2a both sides:[tex]2a - 2a + 29 = 3a - 2a[/tex]=> [tex]29 = 3a - 2a[/tex]Simplify the RHS and change the sides:=> [tex]\bold{a = 29}[/tex]Let's substitute the value of a in 3a + 7u + 9 = 180° to find u.[tex]3a + 7u + 9 = 180\°[/tex]=> [tex]3(29) + 7u + 9 = 180\°[/tex]Simplify the LHS:=> [tex]87 + 9 + 7u = 180[/tex]=> [tex]96 + 7u = 180[/tex]Subtract 96 both sides:=> [tex]96 - 96 + 7u = 180 - 96[/tex]=> [tex]7u = 84[/tex]Divide 7 both sides:=> [tex]\frac{7u}{7} = \frac{84}{7}[/tex]=> [tex]\bold{u = 12}[/tex]