The Triangle and Its Properties
Exercise 6.3
1). Find the value of the unknown x in the following diagrams:
i).
by angle sum property of a triangle
mÐA + mÐB + mÐC = 1800
x + 500 + 600 = 1800
x + 1100 = 1800
x = 1800 – 1100
x = 700
ii).
by angle sum property of a triangle
mÐP + mÐQ + mÐR = 1800
900 + 300 + x = 1800
x + 1200 = 1800
x = 1800 – 1200
x = 600
iii).
by angle sum property of a triangle
mÐX + mÐY + mÐZ = 1800
300 + 1100 + x = 1800
x + 1400 = 1800
x = 1800 – 1400
x = 400
iv).
by angle sum property of a triangle
x + x + 500 = 1800
2x + 500 = 1800
2x = 1800 – 500
2x = 1300
x = 130/2
x = 650
v).
by angle sum property of a triangle
x + x + x = 1800
3x = 1800
x = 1800 /3
x = 600
vi).
by angle sum property of a triangle
x + 2x + 900 = 1800
3x = 1800 – 900
3x = 900
x = 900/3
x = 300
Ans: x = 300
2x = 600
2). Find the value of the unknown x and y in the following figures:
i).
the sum of interior opposite angles = exterior angle
500 + x = 1200
x = 1200 – 500
x = 700
by angle sum property of a triangle
500 + x + y = 1800
500 + 700 + y = 1800
y + 1200 = 1800
y = 1800 – 1200
y = 600
Ans: x = 700
y = 600
ii).
vertically opposite angles are congruent
y = 800
by angle sum property of a triangle
500 + x + y = 1800
500 + x + 800 = 1800
x + 1300 = 1800
x = 1800 – 1300
x = 500
Ans: x = 500
y = 800
iii).
the sum of interior opposite angles = exterior angle
500 + 600 = x
x = 500 + 600
x = 1100
by angle sum property of a triangle
500 + 600 + y = 1800
1100 + y = 1800
y = 1800 – 1100
y = 700
Ans: x = 1100
y = 700
iv).
vertically opposite angles are congruent
x = 600
by angle sum property of a triangle
x + y + 300 = 1800
600 + y + 300 = 1800
y + 900 = 1800
y = 1800 – 900
y = 900
Ans: x = 600
y = 900
v).
vertically opposite angles are congruent
x = 900
by angle sum property of a triangle
x + x + 900 = 1800
2x + 900= 1800
2x = 1800 – 900
2x = 900
x = 900 / 2
x= 450
Ans: x = 450
y = 900
vi).
vertically opposite angles are congruent
x = y
by angle sum property of a triangle
x + x + x = 1800
3x = 1800
x = 1800 /3
x = 600
x = y
y = 600
Ans: x = 600
y = 600
Click here for the solutions of
