Angles of a pentagon are in an arithmetic sequence.
a) What is the sum of the terms of this sequence ?
b) What is the middle term ?
c) If the smallest angle is 40° what is the difference between two adjacent angles?
d) Write the angles as a sequence.
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Answer:The middle term of the AP is 60°
The angles of the triangle are 90° , 60° and 30°
Angles of a right triangle are in arithmetic sequence.
The middle term of the sequence
The angles of the triangle
Let us consider the angles of the triangle be a - d , a , a + d (since they are in AP)
Thus , from the properties of triangle we have ,
Thus , middle term of the AP is 60°
Again, it is given that the triangle is a right angled triangle
Therefore , its largest angle is 90°
Thus , common difference of the AP is 30°
The remaining angle of the triangle is :
Therefore ,the angles of the triangle are 90° , 60° and 30°
Step-by-step explanation:
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