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.

answer: y = -2.5x - 15

              (-6,0)

step-by-step explanation:

if gloria has "carry over" minutes, (that is, any minutes paid for but not used in a month can be applied to her payment for minutes in the next month,) her total usage for the three months is: total minutes = 320 + 243 + 489 = 1052 minutes number of 200 minute blocks = 1052/200 = 5 r52 (that is 5 with a remainder of 52) rounding up the number of 200 minute blocks gives her usage for the three months as 6 blocks. the cost for six blocks is 6 x $25 = $150 she also has 200 - 52 or 148 carry over minutes if gloria pays each month and unused minutes are lost, applying the rounding up procedure to each month gives: first month usage of 320 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 second month usage of 243 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 third month usage of 489 minutes rounds up to 3 blocks of 200 minutes for a payment of 3 x $25 = $75 total payments for the three months are $50 + $50 + $75 = $175 get the plan with carry over minutes!