Atriangle abc is inscribed in a circle, such that ab is a diameter. what are the measures of angles of this triangle if: measure of arc ac = 70°.

Part 1) The measure of angle C is 90°

Part 2) The measure of angle B is 35°

Part 3) The measure of angle A is 55°

Step-by-step explanation:

we know that

The inscribed angle is half that of the arc it comprises.

step 1

Find the measure of angle C

The diameter divide the circle into two equal parts

so

If AB is a diameter

arc AB=180°

∠C=(1/2)[arc AB]

∠C=(1/2)[180°]=90°

step 2

Find the measure of angle B

arc AC=70°

∠B=(1/2)[arc AC]

∠B=(1/2)[70°]=35°

step 3

Find the measure of angle A

The sum of the internal angles of a triangle must be equal to 180 degrees

so

∠A+∠B+∠C=180°

substitute

∠A+35°+90°=180°

∠A=180°-(35°+90°)

∠A=55°

answer:

step-by-step explanation:

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it