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WAEC Mathematics 2014 Paper

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Question : 42

Total: 49

In the diagram, PQR is a straight line, (m + n) = 120^o and (n + r) = 100^o. Find (m + r)

110^o
120^o
140^o
160^o

Solution:

Concept:

Angles on a straight line add up to

180^\circ

.

Explanation:

Since

PQR

is a straight line, the angles at point

Q

satisfy:

m + n + r = 180^\circ

It is given that

m + n = 120^\circ

.

Substitute into the total:

120^\circ + r = 180^\circ

r = 180^\circ - 120^\circ = 60^\circ

Also given

n + r = 100^\circ

.

Substitute

r = 60^\circ

:

n + 60^\circ = 100^\circ

n = 40^\circ

Now use

m + n = 120^\circ

:

m + 40^\circ = 120^\circ

m = 80^\circ

Therefore:

m + r = 80^\circ + 60^\circ = 140^\circ

Answer:

140^\circ

Option C.

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