Question

Need the answer plezzz hurry

Answer 1

The correct option is B .
`m\angle 1+m\angle 3`

Therefore the equivalent expression for ∠4 is

`m\angle 4=m\angle 1+m\angle 3`

Explanation:

Let label the diagram first such that

In ΔPQR ,

∠RPQ = ∠1

∠PQR = ∠2

∠PRQ = ∠3

To Find:

Expression for ∠RQS = ∠4 = ?

Solution:

Exterior Angle Theorem :

The exterior angle theorem states that the exterior angle formed when you extend the side of a triangle is equal to the sum of its non-adjacent angles.

The theorem tells us that the measure of angle RQS is equal to the sum of angles RPQ and PRQ.

`m\angle RQS=m\angle RPQ+m\angle PRQ`

Substituting the angles we get'

`m\angle 4=m\angle 1+m\angle 3`

Therefore the equivalent expression for ∠4 is

`m\angle 4=m\angle 1+m\angle 3`