Question

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Answer 1

Answer:

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

Therefore the equivalent expression for ∠4 is

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

Step-by-step 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

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