In a triangle, the measure of the first angle is twice the measure of the second angle. the measure of the third angle is 64 degrees more than the measure of the second angle. use the fact that the sum of the measures of the three angles of a triangle is 180degrees to find the measure of each angle.

The first angle would be 58°, the second angle would be 29°, and the third angle would be 93°.

We can find this by first writing the angles as expressions in terms of x, where x is the value of the second angle. This means that:

The first angle = 2x, as it is twice the second angle
The second angle = x
The third angle = x + 64, as it is 64° more than the second angle.

Now we can add these expressions together and set them equal to 180°:

2x + x + x + 64 = 180
4x + 64 = 180
4x = 116
x = 29

Now that we know that x = 29, we can substitute it in to our other expressions so that 2x = 2 × 29 = 58°, and x + 64 = 29 + 64 = 93°.

I hope this helps!

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12