a carpenter designs an a-frame chalkboard. its support bars form the legs of an isosceles triangle.
if the measure of base angle abc is 75°, what is m∠bac?

The measure of the angle ∠BAC is 30 degrees.

Step-by-step explanation:

Recall that the sum of the interior angles of every triangle is 180 degrees. The other important geometric property we need to use is that an isosceles triangle has two sides of the same length, and as consequence the angles opposite to those sides has the same measure.

The last property has the common formulation: ‘‘The angles adjacent to the basis of an isosceles triangles have the same measure’’.

With this we know the measure of the other base angle ∠BCA: 75 degrees.

Use the property of the sum of the interior angles of a triangle:

∠ABC + ∠BCA + ∠BAC =180.

Substituting the known values:

75 + 75 + ∠BAC = 180.

Isolating the unknown angle:

∠BAC = 180-150=30.

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answer is:

bottom one is 9

left one is 16

right one is 25