Ihave a test tomorrow and i’m really confused on the ratio of the measures of three angles in a triangle are 2: 3: 4. find the measure of the smallest angle

First, we can note that, whatever these three angles are, their sum is going to give us 180°, since we're talking about the interior angles of a triangle.

What this 3-way ratio is telling us is that, if we split that 180° up into some number of equal-sized pieces, the first angle will take up 2 pieces, the second one will take up 3, and the third one will take up 4. But how do we know the number of pieces that 180° was split up into in the first place? Well, we know we've got 2 pieces, 3 pieces, and 4 pieces, so putting those together gets us a total of 2 + 3 + 4 = 9 pieces!

How big are each of those pieces? If we split 180 up into 9, we find that they're each 180 ÷ 9 = 20°. This means that 2 pieces will be 20 x 2 = 40°, 3 pieces will be 20 x 3 = 60°, and 4 pieces will be 20 x 4 = 80°. So, our three angles are 40°, 60°, and 80°, making 40° the smallest of the three.

(We can check that this is correct by adding the angles together, finding that 40 + 60 + 80 = 100 + 80 = 180°, which is exactly what we wanted.)

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions