Question

Given: mTRV = 60° mTRS = (4x)° Prove: x = 30 What is the missing reason in step 3? substitution property of equality angle addition postulate subtraction property of equality addition property of equality

Answer 1

Answer: Angle addition postulate.

Explanation: If $\angle TRV= 60^{\circ}$ and $\angle TRS=4x^{\circ}$

here, if we have to prove x=30

If there is a condition that TR is a line which meets with the line segment VS at point R then by the Angle addition postulate,  we can say that $\angle TRV+\angle TRS=180^{\circ}$⇒$x=30^{\circ}$

But,

In option (1) substitution property of equality

If there is condition that  $\angle TRV=\angle TRS$

then we can use  substitution property of equality,

And, in this case $4x^{\circ}=60^{\circ}$⇒$x=15^{\circ}$

which is wrong. So, we can not use this property here.

In option (3) subtraction property of equality

There is no use of this property to find the value x.

In option (4) addition property of equality

There is no use of this property to find the value x.

Answer 2

The omitted reason in step 3 should be the angle addition postulate.

• According to the angle addition postulate , the value or measurement of an angle is the sum of all the angles which makes up that segment.

From the diagram attached ;

mTRV = 60 ; ∠TRS = 4x

According to the addition postulate :

mTRV + ∠TRS = 180° (sum of linear pair of angles).

• Though obtaining the value of the missing angle required substituting 30 for the value of x.

• However, it is because of the addition postulate which gives the sum of a linear pair of angles that we were able to establish that mTRV + ∠TRS = 180°.

Hence, the missing reason for the third step is the angle addition postulate.

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