Question

∆XYZ is constructed such that XY = 4 cm, XZ = 8 cm and ∠X = 20⁰. Then, find the sum of measures of ∠Y and ∠X.

Answer 1

Steps of construction:
Step 1: Draw the base line XY of the length 4 cm.

Step 2: Measure the ∠X with your protractor. Make a mark at 20 degrees and draw a line from X passing through the mark.

Step 3: Cut an arc of radius 8 cm on the line passing through the point X. The point where this arc cuts the line is the point Z.

Step 4: Draw a line from Y to point Z to get the required ∆XYZ, as shown below.

From the above construction, measure the angle Y, we see that the measure of ∠Y is 142⁰.

So,
∠X + ∠Y = 20⁰ + 142⁰ = 162⁰