Question

find the values of x,y,a in the following figure .​

Answer 1

Answer:

(i)x=25°, y=80°, z=30°

(ii)x=30°, y=70°, z=110°

Step-by-step explanation:

(i)In ΔPAB,

<BPA+<PAB+<PBA=180°

50°+100°+<PBA=180°

150°+<PBA=180°

<PBA=180°-150°

<PBA=30°

In ΔPBC,

<BPC+<PCB+<PBC=180°

50°+75°+<PBC=180°

125°+<PBC=180°

<PBC=180°-125°

<PBC=55°

<PBA+<ABC=<PBC

30°+<ABC=55°

<ABC=55-30°

<ABC=25°

In ΔABC,

<BAC+<ABC+<ACB=180°

<BAC+25°+75°=180°

<BAC+100=180°

<BAC=180°-100°

<BAC=80°

(ii)In ΔABD,

<BAD+<ABD+<ADB=180°

30°+40°+<ADB=180°

70°+<ADB=180°

<ADB=180°-70°

<ADB=110°

<ADB+<ADC=180°

110°+<ADC=180°

<ADC=180°-110°

<ADC=70°

In ΔADC

<DAC+<ADC+<ACD=180°

<DAC+70°+80°=180°

<DAC+150°=180°

<DAC=180°-150°

<DAC=30°