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