1. ## geometry

1. In the diagram, trangle ABC is inscribed in the circle and AC=AB. The measure of angle BAC is 42 degrees and segment ED is tangent to the circle at point C. What is the measure of angle ACD?

2. If 10 men take 6 days to lay 1000 bricks, how many days will it take 20 men to lay 5000 bricks?

I know the answer is 15 days. Just need help setting the equation up. TY

2. Originally Posted by Brent
1. In the diagram, trangle ABC is inscribed in the circle and AC=AB. The measure of angle BAC is 42 degrees and segment ED is tangent to the circle at point C. What is the measure of angle ACD?

Note that angle ACD = angle BCE. thus, $\angle ACD + \angle BCE + \angle ACB = 180$

$\Rightarrow 2 \angle ACD + \angle ACB = 180$

$\Rightarrow \angle ACD = \frac {180 - \angle ACB}2$

now you can find $\angle ACB$, right (hint: the triangle is isosceles). thus you will find $\angle ACD$

2. If 10 men take 6 days to lay 1000 bricks, how many days will it take 20 men to lay 5000 bricks?

I know the answer is 15 days. Just need help setting the equation up. TY
intuitive approach:

if it takes 10 men 6 days to make 1000 bricks, it will take them 5 times as long to make 5000 bricks, that is, it takes 10 men 30 days to make 5000 bricks. thus, if you double the men, you cut the time in half, and hence, it takes 20 men 30/2 = 15 days to make 5000 bricks

3. Originally Posted by Brent
1. In the diagram, trangle ABC is inscribed in the circle and AC=AB. The measure of angle BAC is 42 degrees and segment ED is tangent to the circle at point C. What is the measure of angle ACD?

2. If 10 men take 6 days to lay 1000 bricks, how many days will it take 20 men to lay 5000 bricks?

I know the answer is 15 days. Just need help setting the equation up. TY

For question 1 you have an isosceles triangle so the two base angles
$\frac{180-42}{2}$

so the angle is 69 degrees, <ABC is an inscribed angle so it is $\frac{1}{2}$ the arc that it intercepts. Arc AC is 138 degrees, Then when a tangent intecepts a circle the arc is half the arc it intercepts so it 69 degrees