Answer:
∠b=133°
∠c=47°
∠d=133°
Step-by-step explanation:
We are given with two lines intersecting at a point and thus forming 4 angles
∠a , ∠b ,∠c and ∠d
Here we must understand the properties of angles formed by two intersecting lines.
Supplementary Angles :
In our image following pairs are supplementary angles
∠a and ∠b
∠b and ∠c
∠c and ∠d
∠d and ∠a
the properties of supplementary angles say that their sum is 180°
Hence if ∠a=47°
∠a+∠b=180°
47°+∠b=180°
∠b=180°-47°
∠b=133°
Vertically opposite angles. When two lines intersects , they form two pairs of vertically opposite angles
here
∠a and ∠c
∠b and ∠d
are vertically opposite angles
The property says that they are equal.
Hence
if ∠a=47° , ∠c=47°
if ∠b=133° , ∠d=133°
4x+6x+2x+4x+6x+2x+10+10
=10x+6x+8x+20
=16x+8x+20
=24x+20
24x+20 is your answer.
