ATTEMPT ALL THE QUESTIONS AT THE BACK OF THE PAGE The table below shows income tax rates for the year 2006

Kwa kuwa EADF ni mstari ulionyooka, jumla ya pembe kwenye mstari ni $180^\circ$.

$$\angle BAD + \angle BAE = 180^\circ$$

Tunajua $\angle BAE = 98^\circ$.

$$\angle BAD = 180^\circ - 98^\circ = 82^\circ$$

Pembe ya nje ya quadrilateral ya mzunguko ni sawa na pembe ya ndani iliyo kinyume.

$$\angle ABC = \angle CDF$$

Tunajua $\angle CDF = 68^\circ$.

$$\angle ABC = 68^\circ$$

Jumla ya pembe zinazopingana katika quadrilateral ya mzunguko ni $180^\circ$.

$$\angle ABC + \angle ADC = 180^\circ$$ $$68^\circ + \angle ADC = 180^\circ$$ $$\angle ADC = 180^\circ - 68^\circ = 112^\circ$$

Tunajua $\angle ADC = 112^\circ$ na $\angle BDC = 45^\circ$.

$$\angle ADB = \angle ADC - \angle BDC$$ $$\angle ADB = 112^\circ - 45^\circ = 67^\circ$$

Jumla ya pembe katika pembetatu ni $180^\circ$.

$$\angle ABD + \angle BAD + \angle ADB = 180^\circ$$ $$\angle ABD + 82^\circ + 67^\circ = 180^\circ$$ $$\angle ABD + 149^\circ = 180^\circ$$ $$\angle ABD = 180^\circ - 149^\circ = 31^\circ$$

Kwa hivyo, $\boxed{\text{a) } \angle ABD = 31^\circ}$.

Tunajua $\angle ABC = 68^\circ$ na $\angle ABD = 31^\circ$.

$$\angle CBD = \angle ABC - \angle ABD$$ $$\angle CBD = 68^\circ - 31^\circ = 37^\circ$$

Kwa hivyo, $\boxed{\text{b) } \angle CBD = 37^\circ}$.