Math Problem Statement

Given that m∠TRV = 60° and m∠TRS = (4x)°, prove that x = 30.

Solution

The problem presented in the image involves solving for xx using the properties of angles, specifically linear pairs. The diagram shows two angles at a point labeled RR, where TRV\angle TRV is given as 6060^\circ, and TRS\angle TRS is (4x)(4x)^\circ. The task is to prove that x=30x = 30.

Given:

  • mTRV=60m\angle TRV = 60^\circ
  • mTRS=(4x)m\angle TRS = (4x)^\circ

To Prove:

  • x=30x = 30

Reasoning Steps:

  1. Given:

    • mTRV=60m\angle TRV = 60^\circ
    • mTRS=(4x)m\angle TRS = (4x)^\circ
  2. Statement 2: TRS\angle TRS and TRV\angle TRV are a linear pair.

    • Reason: Definition of a linear pair.
  3. The missing reason for step 3 likely involves the Linear Pair Postulate, which states that the sum of the measures of angles in a linear pair is 180180^\circ. Therefore, mTRS+mTRV=180m\angle TRS + m\angle TRV = 180^\circ.

Let me solve the problem:

mTRV+mTRS=180m\angle TRV + m\angle TRS = 180^\circ

Substitute the given values:

60+(4x)=18060^\circ + (4x)^\circ = 180^\circ

Solve for xx:

4x=180604x = 180^\circ - 60^\circ 4x=1204x = 120^\circ x=1204=30x = \frac{120^\circ}{4} = 30

Thus, x=30x = 30.

The Missing Reason in Step 3:

The missing reason in step 3 is the Linear Pair Postulate, which states that the sum of the measures of a linear pair of angles is 180180^\circ.


Do you have any questions or need further details?

Here are 5 related questions you might find interesting:

  1. What is the definition of a linear pair of angles?
  2. How do we know that angles on a straight line sum up to 180 degrees?
  3. Can two angles form a linear pair if they are not adjacent?
  4. How would the solution change if mTRVm\angle TRV were 7070^\circ instead of 6060^\circ?
  5. What other angle properties (besides linear pairs) can help in solving geometry problems?

Tip: Always double-check the definitions and postulates relevant to the problem before proceeding with solving it!

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Math Problem Analysis

Mathematical Concepts

Geometry
Linear Pair of Angles
Algebra

Formulas

Sum of angles in a linear pair = 180°

Theorems

Linear Pair Postulate

Suitable Grade Level

Grades 8-10