There are five exams. the student earned grades 84,75,97, and 89 for the first four exams.what grade must the student earn pm the last exam to get an exam avergae of at least 85?

81

Step-by-step explanation:

Given total number of tests are 5

The grades earned by the students in the tests are 84 , 75 , 97 , 89

let the grade earned by the student in the fifth test be x.

Average=

The condition recquired is Average≥85

≥85

≥85

x≥81.

The least grade the student can earn in the last test so that average is not less than 85 is 81

m∠CXA=136°

Step-by-step explanation:

In this problem we know that

Triangle ABC is an isosceles triangle

so

m∠BCA=m∠BAC=44°

Segment AD  bisect angle  m∠BAC

so

m∠BAX=m∠XAC=m∠BAC/2=22°

Segment CE  bisect angle  m∠BCA

so

m∠BCX=m∠XCA=m∠BCA/2=22°

Remember that

The sum of the interior angles of triangle must be equal to 180 degrees

so

In the triangle AXC

m∠XCA+m∠XAC+m∠CXA=180°

we have

m∠XCA=22°

m∠XAC=22°

substitute

22°+22°+m∠CXA=180°

m∠CXA=180°-44°=136°