AD is the bisector of triangle ABC. A straight line is drawn through point D, parallel to side AB

univerkov | February 4, 2021 | education

AD is the bisector of triangle ABC. A straight line is drawn through point D, parallel to side AB and intersecting side AC at point T. Find the angles of triangle ADT, if angle BAC = 72º

Let us find the angles ∠BAD and ∠DAC, which are formed by the bisector AD.

∠BAD = ∠DAC = 1/2 BAC = 72/2 = 36 °.

Since straight lines AB and DT are parallel, the crossed angles are ∠DAT = ∠ADT = 36 °.

Find the angle ∠ATD.

∠ATD = 180 – (36 * 2) = 180 – 72 = 108 °.

Answer: the angles of the triangle ADT are 36 °; 36 ° and 108 °.

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