Finding Angles with Variables Review Combining like terms

Finding Angles with Variables

Review: Combining like terms Only terms with the exact same variables and exponents can be added or subtracted. Leave everything else separate. Example: Note: x 2 = 1 x 2

When solving for angles with variables, still set up an equation and solve for the variable using knowledge of triangles and complementary, supplementary, and vertical angles.

Find the measure of angles ABC and CBD

Find the measure of angles ABC and CBD Since the two angles form a straight line, 2 x + 3 x = 180° they are supplementary and add to 180° Combine like terms Inverse operation Substitute back in to find the actual angles 5 x ÷ 5 x = 180° ÷ 5 = 36° m/ABC = 2 x = 2(36) = 72° m/CBD = 3 x = 3(36) = 108°

Find /KLM and /MLN

Find /KLM and /MLN The angles are complementary because they form a right angle so they add up to 90° 3 y + 10° = 90° Combine like terms 4 y + 10 = 90° Inverse operation 4 y Inverse operation Substitute back in - 10° -10° = 80° ÷ 4 y = 20° m/KLM = 3 y = 3(20) = 60° m/MLN = y+10 = 20+10 = 30°

Find the degrees of each angle

Find the degrees of each angle The angles are vertical so they are equal 10 m + 30 = 20 m - 20 “Inverse operation” -10 m Substitute back in to find the angle -10 m 30 = 10 m – 20 + 20 50 = 10 m ÷ 10 5= m m/ = 10 m+30 = 10(5)+30 = 50 + 30 = 80°

Find the missing angles X Y Z

Find the degrees of each angle The angles in a triangle add to 180° Combine like terms Inverse operation Substitute back in to find the angle 6 x+18 + x+9 + 90 = 180 7 x + 117 = 180 -117 7 x = 63 ÷ 7 x = 9 m/X = 6 x+18= 6(9)+18 = 72° m/Z = x+9 = 9+9 = 18°