# In the Fig. 5.8, we have ∠1 = ∠3 and ∠2 = ∠4. Show that ∠A = ∠C. Solve using Euclid’s axiom

**Solution:**

The figure represents a quadrilateral ABCD.

Given, ∠1 = ∠3 -------------- (1)

Also, ∠2 = ∠4 ---------------- (2)

We have to show that ∠A = ∠C.

On adding (1) and (2),

∠1 + ∠2 = ∠3 + ∠4

By using Euclid’s axiom,

If equals are added to the equals, the wholes are equal.

From the figure,

∠1 + ∠2 = ∠A

∠3 + ∠4 = ∠C

Therefore, ∠A = ∠C

**✦ Try This: **A transversal intersects two lines in such a way that the two interior angle on the same side of transversal are equal.Will the two lines always be parallel?

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

**NCERT Exemplar Class 9 Maths Exercise 5.3 Problem 8**

## In the Fig. 5.8, we have ∠1 = ∠3 and ∠2 = ∠4. Show that ∠A = ∠C. Solve using Euclid’s axiom

**Summary:**

The figure represents a quadrilateral ABCD. In the Fig. 5.8, we have ∠1 = ∠3 and ∠2 = ∠4. By using Euclid’s axiom, it is shown that ∠A = ∠C

**☛ Related Questions:**

visual curriculum