In triangle ABC, it is given that angle A is 59 degrees and angle B is 53 degrees. The altitude from B to line AC is extended until it intersects the line through A that is parallel to segment BC; they meet at K. Calculate the size of angle AKB.

  ∠AKB = 22°

Step-by-step explanation:

Call the point of intersection of BK and AC point P. Then line BK is a transversal to parallel lines AK and BC. Alternate interior angles AKB and PBC will be congruent.

We know that angle PCB is 68°, the difference between 180° and the sum of the two given angles in ΔABC:

  ∠PCB = 180° -∠PAB -∠ABC = 180° -59° -53° = 68°

Since PB is an altitude, ∠CPB is a right angle. Then ∠PBC is the complement of ∠PCB, so is ...

  ∠PBC = 90° -68° = 22°

As we said, this is congruent to ∠AKB, so ...

  ∠AKB = 22°

68°

Step-by-step explanation:

BC is parallel to BK

Angles BCA and BKA are equal

180 - 59 - 53 = 68°

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is