17.Therefore x=[tex]31^\circ[/tex] and y= [tex](\frac{123}{3})^ {\circ}[/tex]
18.Therefore x = 9 units and y = 10.5 units
19.Therefore [tex]x=15^\circ[/tex] and y = 7 units
Step-by-step explanation:
17.
Opposite angles of a parallelogram are equal.
So [tex]3y^{\circ}=123^{\circ}[/tex]
⇒ y= [tex](\frac{123}{3})^ {\circ}[/tex]
and sum of adjacent angle is = [tex]180^{\circ}[/tex]
Therefore, [tex](2x-5)^{\circ} + 123^ {\circ}=180^{\circ}[/tex]
⇒[tex](2x-5)^{\circ} =180^{\circ}-123^ {\circ}[/tex]
⇒[tex]2x^\circ=57^\circ+5^\circ[/tex]
⇒x=[tex]31^\circ[/tex]
Therefore x=[tex]31^\circ[/tex] and y= [tex](\frac{123}{3})^ {\circ}[/tex]
18.
The diagonals of rectangle bisect each other.
so, 2x=x+9
⇔2x- x=9
⇔x = 9 units
Again opposite sides are congruent.
So,3y -9 =y+12
⇔3y - y =12+9
⇔y [tex]=\frac{21}{2}[/tex] units =10.5 units
Therefore x = 9 units and y = 10.5 units
19.
[tex]3x^\circ=45^\circ[/tex] [∵ they are transversal angles]
⇔[tex]x=15^\circ[/tex]
And opposite sides are equal
7y = 4y + 21
⇔7y - 4y = 21
⇔3y = 21
⇔y = 7 units
Therefore [tex]x=15^\circ[/tex] and y = 7 units
