Math Problem Statement

Pada gambar dibawah, besar sudut yang bertolak belakang dengan ∠TOQ adalah?

Solution

The problem asks for the angle that is opposite (or "bertolak belakang") to ∠TOQ based on the provided diagram.

Analysis:

  • The diagram shows several lines intersecting at point OO.
  • The angle ∠TOQ is indicated between the lines TQTQ and OQOQ, and is labeled as xx^\circ.
  • There is another angle near point OO labeled as 2x2x^\circ.
  • Since the two angles form a straight line (linear pair), they must sum to 180180^\circ.

Step-by-step solution:

  1. Since TOQ=x\angle TOQ = x^\circ and SOQ=2x\angle SOQ = 2x^\circ form a linear pair: x+2x=180x + 2x = 180^\circ Solving this gives: 3x=180x=603x = 180^\circ \quad \Rightarrow \quad x = 60^\circ
  2. The problem asks for the angle opposite (bertolak belakang) to ∠TOQ. Since ∠TOQ is 6060^\circ, its opposite angle (which is vertically opposite) is also 6060^\circ.

Thus, the correct answer is: 60\boxed{60^\circ}

Would you like further clarification or more details?

Related questions:

  1. What is a linear pair of angles and how do they relate to straight angles?
  2. How do vertically opposite angles work in intersecting lines?
  3. How can we calculate unknown angles in geometric diagrams using algebra?
  4. Can you explain the difference between complementary and supplementary angles?
  5. How would the diagram change if the angle 2x2x were instead 3x3x?

Tip: Vertically opposite angles are always equal when two lines intersect.

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Math Problem Analysis

Mathematical Concepts

Geometry
Linear Pair of Angles
Vertically Opposite Angles

Formulas

Sum of angles on a straight line = 180°
Vertically opposite angles are equal

Theorems

Linear Pair Theorem
Vertically Opposite Angle Theorem

Suitable Grade Level

Grades 8-10