Given m<ABC=88°.
<ABD=2x and <CBD=x-2.
Soltution. m<ABC is the sum of angles m<ABD and m<CBD.
So, we can setup an equation as
m<ABD + m<CBD = m<ABC.
Plugging values of m<ABD, m<CBD and m<ABC in above equation, we get
2x + x-2 = 88
Combining like terms 2x+x=3x, we get
3x-2=88.
Adding 2 on both sides,
3x-2+2=88+2.
3x=90.
Dividing both sides by 3, we get
3x/3=90/3
x=30.
Plugging value of x=30 in given values of m<ABD and m<CBD
<ABD=2x = 2(30) = 60° and
<CBD=x-2 = x-2 = 30-2 =28°.
Therefore, <ABD =60° and <CBD=28°.