The answers to the problem are:
a) The value of x is : 8
b) ∠ZRB and ∠BTS are not supplementary angles.
c) ∠BST and ∠RSB are complementary angles.
d) ∠ABT is an acute angle
e) SA is not the bisector of the angle ∠ZSY.
Types of Angles
Angles are formed when two lines meet and they are of different types.
acute: this is an angle less than 90°
obtuse: this angle is greater than 90° but less than 180°
reflex: this angle is greater than 180° but less than 360°
Analysis:
∠BRS = 180 - (20X - 22) = 202 - 20X
a) To find x, sum of angles in the triangle = 202-20x + 2x+32 + 5x+10 + 120-10x = 180
364 -23x = 180
23x = 364-180
23x = 184
x = 8
b) ∠ZRB = 20x-22 = 20(8) - 22 = 138°
∠BTS = 2x+32 = 2(8)+32 = 48°
138°+48° = 186° [tex]\neq[/tex] 180°
They are not supplementary
c) ∠BST = 120-10X = 120 - 10(8) = 40°
∠RSB = 5x+10 = 5(8)+10 = 50°
50+40 = 90°. They are complementary
d) ∠ABT = 180 - ∠ABR = 180 - 100 - x = 88°
It is acute since it is less than 90°
e) SA is not an angle bisector, since it dived the angles as 40° and 50° and not equal.
In conclusion, the solution to the questions are:
a) The value of x is : 8
b) ∠ZRB and ∠BTS are not supplementary angles
c) ∠BST and ∠RSB are complementary angles
d) ∠ABT is an acute angle
e) SA is not the bisector of the angle ∠ZSY
Learn more about angles: brainly.com/question/25716982
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