# IGCSE Mathematics Paper-1: Specimen Questions with Answers 58 - 58 of 324

## Question 58

### Describe in Detail

Essay▾In the diagram, the lines AB and CD are parallel. The lines AD and BC intersect at X. Angle XDC = 35° and angle CXD = 120°.

(a) (i) Write down the size of angle BAX.

(ii) Write down the size of angle ABX

(b) Complete the statement: Triangle AXB is ________ to triangle DXC.

(c) AB = 8.3 cm, BX = 5.5 cm and CD = 16.6 cm. Calculate the length of CX.

### Explanation

(a) (i) Here, in angles BAX and CDX are alternate interior angles which will be similar.

So, .

(ii) For :

Here, is given, so .

Now, in any triangle addition of all angles will be

So, in

So, in , will also be , as and are alternate interior angles

(b) Here, Triangle AXB is **similar** to triangle DXC because there all three angles are same in both.

- Two triangles are called as
**congruent triangles**when both have all equal sides and equal angles. - Two triangles are called as
**similar triangles**:

o If all angles are same in both.

o If all pairs of sides are in same proportion.

o If two pairs of sides are in same proportion and one angle is also same in both.

(c) Here, AB = 8.3 cm, BX = 5.5 cm and CD = 16.6 cm are given,

So, formula for similar triangles for side: