Question

find the measures of a and b in the following figure​

Answer 1

Given,

Triangle ABC is given with angles,

∠BAD=$30^{0}$

∠CAD=$50^{0}$

∠ACD=$60^{0}$

To find,

The measures of the unknown angles,

∠ABD =$a^{0}$

∠ADC=$b^{0}$

Solution,

Now, ABC is a triangle.

Sum of all the angles in a triangle = $180^{0}$

So,

∠ABC=$a^{0}$

∠BCA=$60^{0}$

∠CAB=∠DAB+∠CAD=$30^{0}$+$50^{0}$=$80^{0}$

∠ABC+∠BCA+∠CAB=$180^{0}$

$a^{0} + 60^{0} +80^{0} = 180^{0}$

$a^{0}= 180^{0} - 140^{0} \\a^{0}= 40^{0}$

Now,ADC is a sub triangle of ABC.

Therefore,

∠ADC+∠CAD+∠ADC=$180^{0}$

$50^{0} + b^{0} + 60^{0}= 180^{0} \\b^{0} = 180^{0} - 110^{0} \\b^{0} = 70^{0}$

Hence , the measures of a and b are 40 and 60 respectively.

Answer 2

Answer:

angle 30degree and 50 degree and 60 gegree a = 30 degree

answer 60 degree