(1) “Langley’s Problem,” “Right-Angled Quadrilateral”
Author: rindenExecutions: 4138
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Given that ∠ABD = a, ∠DBC = b, ∠ACB = c, and ∠DCA = d in quadrilateral ABCD, find ∠ADB.(Since images cannot be posted on this site, please draw quadrilateral ABCD yourself, identify which sides correspond to a, b, c, and d, and express each problem using (a, b, c, d).) These four angles do not have to be in 10° increments; decimal angles are also acceptable.The values (20, 60, 50, 30) below will disappear when you click “Clear”; enter the angles you want to calculate and click “Calculate.”For problems involving angles other than “Langley Problems,” I’ve also uploaded “Langley Type B Problems” and “Rectangular Triangles” to my “Custom Formulas” section, so please refer to those. You can find them under “Custom Formulas” or “Everyone’s Custom Formulas (Math)” > “Geometry” in the top menu bar.
| ∠ADB＝ | degrees |
When ∠ADB = x < 0, since ∠ADB is an obtuse angle, please consider ∠ADB = 180° + x.The calculation uses ARCTAN (where −90° < ARCTAN < 90°). For example, if the result is X = −25°, then ∠ADB = 180° − 25° = 155°. Just because it’s a whole-angle problem doesn’t mean you’ll get an integer angle if you input an integer angle; for example, when the coordinates are (20, 60, 50, 40), ∠ADB = 17.877...°.
Assuming you know the answer for ∠ADB, the challenge is figuring out which auxiliary lines to draw to arrive at that answer. How to draw the auxiliary lines → that depends on the person’s skill… probably…
Assuming you know the answer for ∠ADB, the challenge is figuring out which auxiliary lines to draw to arrive at that answer. How to draw the auxiliary lines → that depends on the person’s skill… probably…
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