Question

What is the value of x ? Identify the missing justifications.

Answer 1

Answer:

Option D) Angle Addition Postulate, Addition Property of equality

Step-by-step explanation:

we have

m∠PQR=(x-5)°

m∠SQR=(x-7)°

m∠PQS=100°

Remember that

The angle addition postulate, describes that putting two angles side by side with their vertices together creates a new angle whose measure equals the sum of the measures of the two original angles

so

Applying the angle addition postulate

m∠PQR+m∠SQR=m∠PQS

substitute the values

(x-5)°+(x-7)°=100° ------> substitution property

2x-12=100 -----> simplify

Remember that

The Addition Property of Equality, states that if you add the same number to both sides of an equation, the sides remain equal

so

Applying the Addition Property of equality

Adds 12 both sides

2x-12+12=100+12

2x=112

Divide by 2 both sides (Division Property of equality)

x=56

therefore

Option D) Angle Addition Postulate, Addition Property of equality

Answer 2

Answer:  The required value of x is 56.

Step-by-step explanation:  We are given to find the value of x from the figure.

From the figure, we note that ray QR divides angle PQS, where

$m\angle PQR=x-5,~~m\angle SQR=x-7,~~m\angle PQS=100.$

Since QR is dividing angle PQS in two parts, so we must have

$m\angle PQR+m\angle SQR=m\angle PQS\\\\\Rightarrow x-5+x-7=100\\\\\Rightarrow 2x-12=100\\\\\Rightarrow 2x=112\\\\\Rightarrow x=\dfrac{112}{2}\\\\\Rightarrow x=56.$

Thus, the required value of x is 56.