Math Problem Statement

∠1 and ∠2 are vertical angles. If m∠1 = (7x - 18)° and m∠2 = (6x - 8)°, then find the measure of ∠1.

Solution

The problem asks to find the measure of 1\angle 1, given that 1\angle 1 and 2\angle 2 are vertical angles. For vertical angles, their measures are equal.

Information Given:

m1=(7x18)m\angle 1 = (7x - 18)^\circ m2=(6x8)m\angle 2 = (6x - 8)^\circ

Since the angles are vertical angles: 7x18=6x87x - 18 = 6x - 8

Solve for xx:

  1. Subtract 6x6x from both sides: x18=8x - 18 = -8

  2. Add 18 to both sides: x=10x = 10

Find m1m\angle 1:

Substitute x=10x = 10 into the expression for m1m\angle 1: m1=7x18=7(10)18=7018=52m\angle 1 = 7x - 18 = 7(10) - 18 = 70 - 18 = 52

Final Answer:

The measure of 1\angle 1 is: 52\boxed{52^\circ}

Would you like a detailed breakdown of any step?


Here are some related questions to expand your understanding:

  1. What are complementary and supplementary angles, and how are they different from vertical angles?
  2. If m2m\angle 2 was given as (8x12)(8x - 12), how would the solution change?
  3. How can you identify vertical angles in a more complex diagram?
  4. What other properties of vertical angles are useful in geometric proofs?
  5. What happens if x=0x = 0 in problems like this?

Tip: Always verify geometric properties (like equality of vertical angles) before solving equations!

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Math Problem Analysis

Mathematical Concepts

Geometry
Algebra
Linear Equations

Formulas

Vertical angles are equal: m∠1 = m∠2

Theorems

Vertical Angles Theorem

Suitable Grade Level

Grades 7-9