# In triangle ABC, angle B is 45 ‘, and angle C is 15’ less than angle B. Find the outer angle at the vertex A.

September 30, 2021 | education

| Let us determine the value of the angle ACB, which, by condition, is 15 less than the angle ABC.

Angle ACB = 45 – 15 = 30.

Then the angle BAC = (180 – 45 – 30) = 105.

The sought angle CAD is adjacent to the angles of BAC, then the angle of CAD = (180 – BAC) = (180 – 105) = 75.

Second way.

The angle BAC, AO condition, is equal to: BAC = (45 – 15) = 30.

The external angle CAD is equal to the sum of the two internal angles of the triangle that are not adjacent to it.

SAD angle = (ABC + BAC) = 45 + 30 = 75.

Answer: The outside angle at vertex A is 75.

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