The key idea
With parallel lines cut by a transversal, angles are either equal or supplementary. Triangle angles sum to 180°; an exterior angle equals the two far interior angles. An n-sided polygon's interior angles sum to 180(n−2), and the exterior angles of any convex polygon sum to 360°.
The trap
Setting two angles equal when they're supplementary.
Can Desmos do it?
No graph will find an angle. Name the angle relationship, then solve.
College Board skill: Lines, angles, and triangles · Geometry and Trigonometry
One question from each level. The drill has 12 at every level, and moves you up after four right in a row.
Level 1 · Warm-up
What is the measure, in degrees, of each interior angle of a regular polygon with 10 sides?
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Answer: 144The interior angles sum to 180(10−2)=1440 degrees, shared equally by 10 angles: 101440=144. (Or: each exterior angle is 10360=36, and 180−36=144.)
Level 2 · Test level
Two parallel lines are cut by a transversal. Two of the angles formed are same-side interior angles (on the same side of the transversal, between the parallel lines), with measures (7x−12)° and (3x+122)°. What is the measure, in degrees, of the larger of these two angles?
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Answer: 143Same-side interior angles are supplementary: (7x−12)+(3x+122)=180. Solving gives x=7, so the angles measure 37° and 143°. The larger is 143°.
Level 3 · Beyond the test
In triangle ABC, AB=AC. Point D lies on BC so that AD=BD. If angle DAC measures 6°, what is the measure, in degrees, of angle ABC?
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Answer: 58Let angle ABC=x. Then angle ACB=x (since AB=AC) and angle BAD=x (since AD=BD). Angle BAC=x+6, so (x+6)+x+x=180 and x=58.
Practice all 36 questions
Answer in the drill to get instant feedback, climb the levels, and feed your misses into Tailored practice. Free, no account.
Circle equationsCompleting the square for center and radius.36 questions, 3 levelsArcs, sectors, and radiansArc length, sector area, radians and inscribed angles.36 questions, 3 levelsSimilar figures and scale factorsScale factors for lengths, areas and volumes.36 questions, 3 levelsRight-triangle trig and complementsSOH CAH TOA, complements and scale factors.36 questions, 3 levelsSpecial right triangles45-45-90 and 30-60-90 side patterns.36 questions, 3 levelsVolume and surface areaVolume formulas, percent changes and displacement.36 questions, 3 levels