The bisector CD is drawn in an isosceles triangle ABC with base AC. Find the angles of triangle ABC

| September 3, 2021 | education

The bisector CD is drawn in an isosceles triangle ABC with base AC. Find the angles of triangle ABC if the angle ADC is: 1) 60 °; 2) 75 °; 3) α.

Let in the triangle ADC <ADC = <d, <BAC = <a, <DCA = <c / 2, and since in the triangle ABC <BAC = <BCA = <a = <c, we rewrite the above equalities for the triangle ADC:

<DCA = <c / 2 = <a / 2, <a + <a / 2 + <d = 180 °, <a * (3/2) = 180 ° – <d.

Whence the angle at the base of the triangle ABC <a = (180 ° – <d) * 2/3.

1) <d = 60 °; <a = (180 ° – <d) * 2/3 = (180 ° – 60 °) * 2/3 = 120 ° * 2/3 = 80 °. Angles of triangle ABC: <a = <c = 80 °, <ABC = <b = 180 ° – 80 ° – 80 ° = 20 °.

2) <d = 75 °; <a = <c = (180 ° – 75 °) * 2/3 = 105 ° * 2/3 = 70 °, <b = 180 ° – 70 ° – 70 ° = 40 ° …

3) <d = α. <a = <c = (180 ° – α) * 2/3, <b = 180 – 2 * <a = 60 – 2/3 * α



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