The value of [tex]m\angle2[/tex] is [tex]132[/tex] and the value of [tex]y[/tex] is [tex]30[/tex].
19) In this question given that,
[tex]m\angle1=x+10[/tex]
[tex]m\angle2=3x+18[/tex]
We have to find the value of [tex]m\angle2[/tex].
As we know that the value of straight line is [tex]180^o[/tex].
From the given figure we can see that
[tex]m\angle1+m\angle2=180^o[/tex]
Now putting the value of [tex]m\angle1[/tex] and [tex]m\angle2[/tex] in the [tex]m\angle1+m\angle2=180^o[/tex].
[tex]x+10+3x+18=180^o[/tex]
Now simplifying the expression.
[tex]4x+28=180^o[/tex]
Subtract [tex]28[/tex] on both side
[tex]4x+28-28=180^o-28[/tex]
[tex]4x=152[/tex]
Divide by [tex]4[/tex] on both side
[tex]\frac{4}{4}x=\frac{152}{4}[/tex]
[tex]x=38[/tex]
We have to find the value of [tex]m\angle2[/tex].
As we know that [tex]m\angle2=3x+18[/tex].
Now putting the value of [tex]x[/tex] in the given value of [tex]m\angle2[/tex].
[tex]m\angle2=3\times38+18[/tex]
[tex]m\angle2=114+18\\[/tex]
[tex]m\angle2=132[/tex]
Hence, the value of [tex]m\angle2[/tex] is [tex]132[/tex].
20) In this question we have to find the value of [tex]y[/tex].
As we know that the value of straight line is [tex]180^o[/tex].
From the given figure we can see that
[tex]2y^o+(3y+30)^o=180^o[/tex]
Now solving the expression to find the value of [tex]x[/tex].
[tex]2y^o+3y^o+30^o=180^o[/tex]
Simplifying the expression.
[tex]5y^o+30^o=180^o[/tex]
Subtract [tex]30^o[/tex] on both side
[tex]5y^o+30^o-30^o=180^o-30^o[/tex]
Simplifying
[tex]5y^o=150^o[/tex]
Divide by [tex]5[/tex] on both side
[tex]\frac{5}{5}y^o=\frac{150^o}{5}[/tex]
[tex]y^o=30^o[/tex]
Hence, the value of [tex]y[/tex] is [tex]30[/tex].
To learn more about angle link is here
https://brainly.com/question/28451077
#SPJ1
