# In an isosceles triangle, the outer angle at the apex opposite to the base is 130 degrees. Find the angles of this triangle 2.

**In an isosceles triangle, the outer angle at the apex opposite to the base is 130 degrees. Find the angles of this triangle 2. In the right-angled triangle ACB (angle C = 90 degrees) the height CD is drawn. Hypotenuse AB = 10cm, angle CBA = 30g. Find BD.**

1). Angle B – the angle at the apex opposite to the base is 180 ° – 130 ° = 50 °;

The angles at the base of an isosceles triangle A and C are equal, which means

<A = <C = (180 ° – 50 °): 2 = 65 °;

2). In a right-angled triangle AB – hypotenuse, AB = 10 cm; <B = 30 °;

AC – leg, lying opposite an angle of 30 °, then AC = 1/2 AB;

AC = 1/2 * 10 = 5 (cm);

By the Pythagorean theorem: BC² = AB² – AC²; BC² = 100 – 25 = 75 (²); BC = √75 (cm);

In a right-angled triangle BCD CD is a leg opposite to an angle of 30 °, CB is a hypotenuse;

means СD = 1/2 CB = 1/2 * √75;

BD² = BC² – CD²; BD² = 75 – 1/4 * 75; BD² = 3/4 * 75; BD = √ (3 * 3 * 25/4);

BD = (3 * 5) / 2; BD = 7.5 cm.