Use complementary, supplementary, vertical, and adjacent angle relationships, including the opposite (equal) and consecutive (supplementary) angles of a parallelogram.
Free, timed SHSAT practice sets on angle relationships— every question includes a full worked explanation, and there's no account required.
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Learn the four angle sums, then set up one equation.
When the angles are expressions, write the equation and solve. Vertical angles \((2x + 10)^\circ\) and \((3x - 5)^\circ\) give \(2x + 10 = 3x - 5\), so \(x = 15\) and each angle is \(40^\circ\).
Common traps: mixing up complementary (90) and supplementary (180), using \(360^\circ\) for a straight line, and stopping at \(x\) when the question asks for the angle. Always plug \(x\) back in.
Supplementary angles add to \(180^\circ\), so the other angle \(= 180 - 69 = 111^\circ\). (Subtracting from \(90^\circ\) (the rule for complementary angles) gives \(21^\circ\). Subtracting from \(360^\circ\) (a full turn) gives \(291^\circ\). Thinking supplementary angles are equal gives \(69^\circ\).)
Vertical angles are equal, so \(2x + 16 = 3x - 41\), which gives \(x = 57\). Each angle \(= 2(57) + 16 = 130^\circ\). (Stopping at \(x = 57\) gives 57, not the angle. Finding the angle next to it, \(180 - 130\), gives \(50^\circ\). Setting the two expressions to add to \(180^\circ\) gives \(x = 41\) and an angle of \(98^\circ\).)
Angles around a point add to \(360^\circ\), so \(x = 360 - 48 - 56 - 78 = 178\). (Forgetting to subtract 78 gives \(360 - 48 - 56 = 256\). Stopping at the sum \(48 + 56 + 78\) gives 182. Assuming all four angles are equal gives \(360 \div 4 = 90\).)