Question

If Angle DAC = 30degree Find the angles of triangle ABC ​

Answer 1

Answer:

Step-by-step explanation:

< A = 40+30 = 70 degrees

< B = 90-40 = 50 degrees ( < PBC = 90 because P||Q and given, <C =90 , BC is transversal )

<C = 180 - 70-50 (sum of angles in a triangle = 180)

< C = 60

Answer 2

$\mathfrak{\huge{\underline{Answer:}}}$

$\textbf{\underline{\underline{In\:Triangle\: ADC }}}$

$\angle\:A = 30^{\circ}$

$\angle\:D = 90^{\circ}$

[Sum of All angles of Triangle = $180^{\circ}$ ]

$\implies\: \angle\: A + \angle\: B + \angle C = {180}^{\circ}$

$\implies\: {30}^{\circ} + {90}^{\circ} + \angle\: C = {180}^{\circ}$

$\implies\: {120}^{\circ} + \angle\: C = {180}^{\circ}$

$\implies \: \angle\:C = 180^{\circ} - 120^{\circ}$

$\implies\: \angle\:C = 60^{\circ}$

$\textbf{\underline{\underline{In\:Triangle\: ABD}}}$

$\angle\:A = {40}^{\circ}$

$\angle\:D = {90}^{\circ}$

$\textbf{\underline{\underline{In\:Triangle\: ABD}}}$

[Sum of All angles of Triangle = $180^{\circ}$ ]

$\implies\: \angle\:A + \angle\:B + \angle\:D = {180}^{\circ}$

$\implies\: {40}^{\circ} + \angle\:B + {90}^{\circ} = \:{180}^{\circ}$

$\implies\:{130}^{\circ}+ \angle\:B =\: {180}^{\circ}$

$\implies\: \angle\:B = \: {180}^{\circ} - {130}^{\circ}$

$\implies\: \angle\:B ={50}^{\circ}$

$\textbf{\underline{\underline{In\:Triangle\: ABC}}}$

$\angle\:A = {40}^{\circ} + {30}^{\circ} =\: 70^{\circ}$

$\angle\:B = {50}^{\circ}$

$\angle\:C = {60}^{\circ}$