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# In the Fig. 5.1, if ∠1 = ∠3, ∠2 = ∠4 and ∠3 = ∠4, write the relation between ∠1 and ∠2, using an Euclid’s axiom

**Solution:**

Given, ∠1 = ∠3, ∠2 = ∠4 and ∠3 = ∠4

We have to write the relation between ∠1 and ∠2 using an Euclid’s axiom.

Euclid’s first axiom states that the things which are equal to the same thing are equal to one another.

∠1 = ∠3

Also, ∠3 = ∠4

Now, ∠1 = ∠3 = ∠4

Given, ∠2 = ∠4

So, ∠1 = ∠2 = ∠3 = ∠4

Therefore, all the angles are equal to one another.

**✦ Try This:** If ∠1 = 120°, find the measures of : ∠2, ∠3, ∠4, ∠5, ∠6, ∠7 and ∠8. Give reasons.

**☛ Also Check: **NCERT Solutions for Class 9 Maths Chapter 5

**NCERT Exemplar Class 9 Maths Exercise 5.3 Sample Problem 3**

## In the Fig. 5.1, if ∠1 = ∠3, ∠2 = ∠4 and ∠3 = ∠4, write the relation between ∠1 and ∠2, using an Euclid’s axiom

**Summary:**

In the Fig. 5.1, if ∠1 = ∠3, ∠2 = ∠4 and ∠3 = ∠4, the relation between ∠1 and ∠2, using Euclid’s first axiom we observe that all the angles are equal to one another

**☛ Related Questions:**

- In Fig. 5.2, we have : AC = XD, C is the mid-point of AB and D is the mid-point of XY. Using an Eucl . . . .
- Two salesmen make equal sales during the month of August. In September, each salesman doubles his sa . . . .
- It is known that x + y = 10 and that x = z. Show that z + y = 10. Solve using Euclid’s axiom

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