Question

In the following figure,find angle b​

Answer 1

Step-by-step explanation:

angle dce = 50°

angle dce = angle c ( vertically opposite angle )

therefore , angle c = 50°

angle fac + bac = 180 ° ( angles in a linear pair )

110° + bac = 180°

bac = 180° - 110°

bac = 70°

therefore angle a = 70°

in ∆ abc ,

a + b + c = 180° ( property of a traingle )

70° + b + 50° = 180 °

120 ° + b = 180°

b = 180 - 120

therefore , b = 60°

Answer 2

Step-by-step explanation:

Given:

∠$FAE=110^{o}$

∠$DCE=50^{o}$

To Find: ∠$ABC$

Calculation:

When there is intersection of two lines, Vertically opposite angles are equal.

Here, ∠$DCE=$∠$ACB=50^{o}$

Now when two lines intersect, the adjacent angles form linear pair and their sum is $180^{o}$. This linear pair form a straight line.

Here, ∠$BAC+$∠$FAE=180^{o}$

Therefore, ∠$BAC=180^{o} -110^{o} =70^{o}$

From property of triangle, in Δ$ABC$:

∠$ABC+$∠$BCA$+∠$CAB=180^{0}$

So, ∠$ABC=180^{o} -(70^{o} +50^{o} )=180^{o} -120^{o} =60^{o}$

∠$B=60^{o}$