Question

Can someone please help me with this?

Answer 1

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°