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WAEC Mathematics 2018 Paper

Question : 43

Total: 50

^{\circ}

^{\circ}

^{\circ}

Solution:

Concept:

Use the given pair sums to solve for each unknown angle.

Since

m

n

, and

r

are angles on the straight line

PQ

, their sum is

180^\circ

, which helps verify the result.

Explanation:

Let the three given equations be:

m+n=110^\circ

... (1)

n+r=130^\circ

... (2)

m+r=120^\circ

... (3)

Add equations (1) and (3):

(m+n)+(m+r)=110^\circ+120^\circ

2m+n+r=230^\circ

Using

n+r=130^\circ

from (2):

2m+130^\circ=230^\circ

2m=100^\circ

m=50^\circ

From equation (1):

n=110^\circ-m=110^\circ-50^\circ=60^\circ

From equation (2):

r=130^\circ-n=130^\circ-60^\circ=70^\circ

Thus the ratio is:

m:n:r=50^\circ:60^\circ:70^\circ

Divide each term by

10^\circ

m:n:r=5:6:7

Answer:

5:6:7

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