Math Problem Statement

Find the values of x and y in the given diagram.

Solution

To solve for the values of xx and yy in this diagram, we will analyze the angles and relationships in the context of the given information.

Step 1: Analyzing the Given Information

  1. BGC\angle BGC is labeled as (13x)(13x)^\circ.
  2. CGD\angle CGD is 3838^\circ.
  3. AGF\angle AGF is labeled as yy^\circ.
  4. The right angle symbol at AGC\angle AGC indicates it is 9090^\circ.

Step 2: Using Angle Relationships

Since lines intersect at point GG and we have angles around this intersection, we can use the fact that:

  • The sum of angles around a point is 360360^\circ.

Therefore, we have: BGC+CGD+DGE+EGF+FGA+AGC=360\angle BGC + \angle CGD + \angle DGE + \angle EGF + \angle FGA + \angle AGC = 360^\circ

Step 3: Applying the Known Angles

From the given information:

  • AGC=90\angle AGC = 90^\circ
  • CGD=38\angle CGD = 38^\circ
  • Let’s assume BGC=13x\angle BGC = 13x and FGA=y\angle FGA = y.

Since the sum of angles around GG is 360360^\circ, we can write the equation:

90+13x+38+y=18090^\circ + 13x + 38^\circ + y = 180^\circ

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Math Problem Analysis

Mathematical Concepts

Angle Relationships
Algebra

Formulas

Sum of angles around a point = 360°

Theorems

Sum of angles around a point

Suitable Grade Level

Grades 8-10