# In an isosceles triangle, the outer apex angle opposite the base is 130 °. Find the smaller of the given triangle

October 2, 2021 | education

| Given:

isosceles triangle ABC,

the outer angle at apex A is 130 °,

АС – base,

AB and BC – lateral sides.

Find the degree measures of angle A and angle C -?

Solution:

1) If the outside angle at the vertex A is 130 °, then

angle ABC = 180 ° – 130 °;

angle ABC = 50 °;

2) consider the triangle ABC. The sum of the degree measures of the angles of any triangle is 180 ° and the angle A = angle C, as the triangle ABC is isosceles. Hence:

angle A + angle B + angle C = 180 °;

angle A + angle C = 180 ° – 50 °;

angle A + angle C = 130 °;

angle A = angle C = 130 ° / 2;

angle A = angle C = 65 °.

Answer: 65 degrees; 65 degrees.

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