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Example 1: Find the value of x in the diagram. 37o x These are vertical angles, or opposite angles made by intersecting lines. Relationship: Vertical angles are equal in measure. x = 37o Example 2: Find the value of x in the diagram. 120o 2x Relationship: Vertical angles are equal in measure. Solve equation for x. 2x = 120o 2 2 x = 60o Example 3: Find the value of x in the diagram. 3x - 10 50o Solve equation for x. Relationship: Vertical angles are equal in measure. 3x – 10 = 50o + 10 +10 3x 3 = 60 3 x = 20o Example 4: Find the value of x in the diagram. x 53o These are supplementary angles. Relationship: Supplementary angles add to 180o. Solve equation for x. x + 53o = 180o - 53 - 53 x = 127o Example 5: Find the value of x in the diagram. 10x 80o Relationship: Supplementary angles add to 180o. Solve equation for x. 10x + 80o = 180o - 80 - 80 10x 10 = 100o 10 x = 10o Example 6: Find the value of x in the diagram. x x + 48 Relationship: Supplementary angles add to 180o. Solve equation for x. x + x + 48o = 180o 2x + 48o = 180o - 48 - 48 2x = 132o 2 2 x = 66o Example 7: Find the value of x in the diagram. x 15o These are complementary angles. Relationship: Complementary angles add to 90o. Solve equation for x. x + 15o = 90o - 15 - 15 x = 75o Example 8: Find the value of x in the diagram. 63o 3x Solve equation for x. Relationship: Complementary angles add to 90o. 3x + 63o = 90o - 63 - 63 3x = 27 3 3 x = 9o Example 9: Find the value of x in the diagram. x + 16o x Relationship: Complementary angles add to 90o. Solve equation for x. x + x + 16o = 90o 2x + 16o = 90o - 16 - 16 2x = 74 2 2 x = 37o