Mathematics Questions & Answers - Free Online Practice

1,256.

In the diagram, STUV is a straight line. < TSY = < UXY = 40^o and < VUW = 110^o. Calculate < TYW

150^o

140^o

130^o

120^o

View answer & explanation

Correct answer is A

< TUW = 110^o = 180^o (< s on a straight line)

< TUW = 180^o - 110^o = 70^o

In \(\bigtriangleup\) XTU, < XUT + < TXU = 180^o

i.e. < YTS + 70^o = 180

< XTU = 180 - 110^o = 70^o

Also < YTS + < XTU = 180 (< s on a straight line)

i.e. < YTS + < XTU - 180(< s on straight line)

i.e. < YTS + 70^o = 180

< YTS = 180 - 70 = 110^o

in \(\bigtriangleup\) SYT + < YST + < YTS = 180^o(Sum of interior < s)

SYT + 40 + 110 = 180

< SYT = 180 - 150 = 30

< SYT = < XYW (vertically opposite < s)

Also < SYX = < TYW (vertically opposite < s)

but < SYT + < XYW + < SYX + < TYW = 360

i.e. 30 + 30 + < SYX + TYW = 360

but < SYX = < TYW

60 + 2(< TYW) = 360

2(< TYW) = 360^o - 60

2(< TYW) = 300^o

TYW = \(\frac{300}{2}\) = 150^o
< SYT

1,257.

From the diagram, Which of the following statements are true? i. m = q ii. n = q iii. n + p = 180^o iv. p + m = 180^o

i and iii

i and iv

ii and iii

ii and ic

View answer & explanation

Correct answer is A

No explanation has been provided for this answer.

1,258.

The graph represents the relation y = x\(^2\) - 3x - 3. What is the equation of the line of symmetry of the graph?

y = 0.5

x = 1.0

x = 1.5

y = 4.6

View answer & explanation

Correct answer is C

No explanation has been provided for this answer.

1,259.

In the diagram, /MN/, /OP/, /QOP/ = 125o. What is the size of < MQR?

11^o

120^o

130^o

160^o

View answer & explanation

Correct answer is B

< NOP = 180 - 125 = 55^o(< s on a straight line)

But < NOP = < ONM (alternate < s)

< ONM = 55^o

< M + < N + < MQN = 180^o (sum of interior < s of a \(\bigtriangleup\)) i.e

65^o + 55^o + < MQN = 180

< MQN = 180 - 12o = 60

< MQR + < MQN = 180 (< s on straight line)

< MQR + 60 = 180

< MQR + 60 = 180

< MQR = 180 - 60

= 120^o