Given:
A figure of a parallelogram.
The vertex angles are [tex](12b+8)^\circ,(5b+2)^\circ,2a^\circ[/tex].
To find:
The values of a and b.
Solution:
We know that the pairs of consecutive angles of a parallelogram are supplementary angles. It mean their sum is 180 degrees.
[tex](12b+8)^\circ+(5b+2)^\circ=180^\circ[/tex] (Supplementary angles)
[tex](17b+10)^\circ=180^\circ[/tex]
[tex]17b+10=180[/tex]
Subtract 10 from both sides.
[tex]17b=180-10[/tex]
[tex]17b=170[/tex]
Divide both sides by 17.
[tex]b=\dfrac{170}{17}[/tex]
[tex]b=10[/tex]
Now,
[tex](5b+2)^\circ=(5(10)+2)^\circ[/tex]
[tex](5b+2)^\circ=(50+2)^\circ[/tex]
[tex](5b+2)^\circ=52^\circ[/tex]
And,
[tex](5b+2)^\circ+2a^\circ=180^\circ[/tex] (Supplementary angles)
[tex]52^\circ+2a^\circ=180^\circ[/tex]
[tex]2a^\circ=180^\circ-52^\circ[/tex]
[tex]2a^\circ=128^\circ[/tex]
Divide both sides by 2.
[tex]a^\circ=\dfrac{128^\circ}{2}[/tex]
[tex]a^\circ=64^\circ[/tex]
[tex]a=64[/tex]
Therefore, the value of a is 64 and the value of b is 10.