1.2.2 Angles and Lines II, PT3 Practice


Question 6:
In Diagram below, PQRST is a straight line. Find the value of x.

Solution:
Interior angle of  R = ( 180 o 76 o ) ÷ 2 = 52 o x = exterior angle of  R   ( corresponding angles ) Hence,  x = 76 o + 52 o = 128 o


Question 7:
In Diagram below, find the value of y.



Solution:


A B C = B C D    = 108 o  (alternate angle) y o + 130 o + 108 o = 360 o   y o = 360 o 238 o   y o = 122 o


Question 8:
In Diagram below, PSR and QST are straight lines.
Find the value of x.

Solution:
UST+STV= 180 o UST= 180 o 116 o = 64 o PST=QSR x o +UST= 135 o x o +UST= 135 o x o = 71 o x=71


Question 9:
In Diagram below, PWV is a straight line.

(a) Which line is perpendicular to line PWV?
(b) State the value of  ∠ RWU.

Solution:
(a) SW

(b) ∠ RWU = 13o + 29o + 20o = 62o

 


Question 10:
In Diagram below, UVW is a straight line.


(a) Which line is parallel to line TU?
(b) State the value of  ∠ QVS.

Solution:
(a) QV

(b) ∠ QVS = 8o + 18o = 26o

 

1.2.1 Angles and Lines II, PT3 Practice


1.2.1 Angles and Lines II, PT3 Practice

Question 1:
In Diagram below, PQRS, ABQC and KRL are straight lines.
Find the value of x.

Solution:


K R B + A B R = 180 o Sum of interior angles K R B + 105 o = 180 o K R B = 180 o 105 o K R B = 75 o B R Q = 40 o Corresponding angle x o = S R L = K R Q Vertically opposite angle x o = 75 o + 40 o = 115 o x = 115


Question 2:
(a) In Diagram below, PQR and SQT are straight lines.
Find the value of x.

(b) In Diagram below, PQRS is a straight line. Find the value of x.
Solution:
(a)
P Q T = R Q S x o + 90 o = 155 o x o = 155 o 90 o = 65 o x = 65

(b)
Q R T = 57 o x o + 2 x o = 180 o 57 o 3 x o = 123 o x o = 123 o 3 x o = 41 o x = 41


Question 3:
In Diagram below, PQR is a straight line. Find the value of x.
Solution:

x o = Q R T + T R S Q R T = 40 o T R S = 180 o 135 o = 45 o Hence, x o = 40 o + 45 o x o = 85 o x = 85


Question 4:
In Diagram below, find the value of x.
Solution:
40o + 80o + xo + xo = 180o
2xo = 180o – 120o
2xo = 60o
x= 30o
 x = 30


Question 5:
In Diagram below, PQR is an isosceles triangle and QRS is a straight line.
Find the values of x and y.

Solution:
P R Q = 180 o 110 o = 70 o P R Q = P Q R = 70 o y o = 180 o 70 o 70 o = 40 o y = 40 x o = 110 o 40 o = 70 o x = 70
 
 

1.1 Angles and Lines II


1.1 Angles and Lines II
 
Identifying Parallel, Transversals, Corresponding Angles, Alternate Angles and Interior Angles
(A) Parallel lines
Parallel lines are lines with the same direction. They remain the same distance apart and never meet.


(B) Transversal lines
A transversal is a straight line that intersects two or more straight lines.



(C) 
Alternate angles




(D) Corresponding angles



(E) Interior angles



PT3 Smart TIP

Alternate angles are easily identified by tracing out the pattern “Z” as shown.


Corresponding angles are easily identified by the pattern “F” as shown.





Interior angles are easily identified by the pattern “C” as shown.

Example 1:
In Diagram below,PQ is parallel to RS. Determine the value of y.

Solution:

Construct a line parallel to PQ and passing through W.
= 40o and b = 50o← (Alternate angles)
= a + b
  = 40o+ 50o
   = 90o


Example 2:
In Diagram below, PSQ and STU are straight lines. Find the value of x.
Solution:
W S Q = 180 o 150 o = 30 o Supplementary angle X T U = W S Q + x Corresponding angle 75 o = 30 o + x x = 75 o 30 o x = 45 o x = 45