The height CD is drawn in an isosceles triangle ABC with base AC. Find the angles of a triangle if the angle is ABC = 40 °.

| May 25, 2021 | education

We know from the condition that a given triangle is isosceles. From the property of an isosceles triangle, it is known that the angles at the base of an isosceles triangle are equal to each other.

We know the apex angle – it is equal to 40 °. It is also known that the height is lowered to the base. In an isosceles triangle, the height is also a bisector and divides the 40 ° angle across the floor by 20 °.

Consider a triangle formed by the height, half the base, and the side of the triangle.

One of its angles is 20 °, the angle is 90 ° (since the perpendicular is lowered to the base), we will find the degree measure of the third angle.

The angles of a triangle add up to 180 °.

180 ° – (20 ° + 90 °) = 180 ° – 110 ° = 70 °.

Answer: 70 ° angles at the base.



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