Here, we are given the measures ∠A and ∠C.
We know that the sum of all the angles of a triangle is 180∘. Hence, we can find the measure of angle B.
∠B = 180∘ - ( ∠A + ∠C ) = 180∘ - ( 75∘ + 55∘ ) = 50∘
Now, we have the following:
Length of side AB = 4 cm, measure of angle A = 75∘ and measure of angle B = 50∘
With these information in hand, it is possible to construct a triangle, as explained below.
Step 1:
Draw the base line AB of the length 4 cm.
Step 2:
Measure the angle A with your protractor. Make a mark at 75 degrees and draw a line from A passing through the mark.
Step 3:
Measure the angle B with your protractor. Make a mark at 50 degrees and draw a line from B passing through the mark.
Step 4:
Name the point of intersection of these two lines as C and the △ABC is complete, as shown below.
Now, from the above construction we see that the length of side AC is 4.2 cm and the length of side BC is 5 cm.
Hence, the sum of other two sides of △ABC = BC + AC = 4.2 cm + 5 cm = 9.2 cm