Which relationship is always true for the angles x, y, and z of triangle abc? a triangle is shown with a leg extending past the top vertex. the vertices are labeled abc. angle y is located inside the triangle at vertex b. angle z is located inside the triangle at vertex c. angle x is located outside the triangle between side ac and the extended leg. x + z = y y + z = x x + y + z = 180 degrees x + y + z = 90 degrees

y+z=x

Step-by-step explanation:

we know that

The Exterior Angle Property of a Triangle states that the measure of exterior angle of a triangle is equals to the sum of measures of its interior opposite angles

In this problem

Angle y and angle z are interior angles of triangle ABC and angle x is a exterior angle of triangle ABC

therefore

Applying the Exterior Angle Property of a Triangle

y+z=x

4sqrt5

step-by-step explanation:

the base has dimensions of 8 x 4, so the diagonal is 64 + 16 square rooted or 4sqrt5.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for