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Heptagon diagonal intersection (Posted on 2025-05-13)

Let ABCDEFG be a regular heptagon. Find the measure of the smaller angle of intersection between AD and CF.

No Solution Yet Submitted by Danish Ahmed Khan

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| Comment 1 of 2

Each angle of the heptagon is (180 - 360/7)° = 128.571428571429°.

Since BC is parallel to AD, angle CDA is the supplement of BCD, and therefore 51.4285714285714°.

Call the intersection H.

Angle CHD is twice the complement of that, as triangle CHD can be considered an isosceles triangle that is two leg-to-leg(back-to-back) right triangles.

Twice the complement of 51.4285714285714° is 77.1428571428571°, which is the desired answer. This is (540/7)°.

Confirmed by construction with Geometers Sketchpad.

Posted by Charlie on 2025-05-13 12:04:42

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