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In Fig. 6.27,
(i) ∠TPQ = ∠ ___ + ∠ _
(ii) ∠UQR = ∠ _ + ∠ _
(iii) ∠PRS = ∠ _ + ∠ ___

In Fig. 6.27, (i) ∠TPQ = ∠ _____ + ∠ _____ (ii) ∠UQR = ∠ _____ + ∠ _____ (iii) ∠PRS = ∠ _____ + ∠ _____

Solution:

Given, the figure represents a triangle PQR.

We have to fill in the blanks to make the statement true.

We observe that P, Q and R are produced to U, S and T.

Exterior angles are defined as the angles formed between the side of the polygon and the extended adjacent side of the polygon.

From the figure,

The exterior angles are TPQ, UQR and PRS.

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two opposite interior angles of the triangle.

By the exterior angle property,

(i) ∠TPQ = ∠PQR + ∠PRQ

(ii) ∠UQR = ∠QRP + ∠QPR

(iii) ∠PRS = ∠RPQ + ∠RQP

✦ Try This: In the given figure, ∠3 and∠4 are exterior angles of quadrilateral ABCD at point B and D, and ∠A = ∠2, ∠C = ∠1, prove that ∠3 + ∠4 = ∠1 + ∠2.

In the given figure, ∠3 and∠4 are exterior angles of quadrilateral ABCD at point B and D, and ∠A = ∠2, ∠C = ∠1, prove that ∠3 + ∠4 = ∠1 + ∠2

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6

NCERT Exemplar Class 7 Maths Chapter 6 Problem 69

In Fig. 6.27, (i) ∠TPQ = ∠ ___ + ∠ _ (ii) ∠UQR = ∠ _ + ∠ _ (iii) ∠PRS = ∠ _ + ∠ ___

Summary:

In Fig. 6.27, (i) ∠TPQ = ∠PQR + ∠PRQ, (ii) ∠UQR = ∠QRP + ∠QPR, (iii) ∠PRS = ∠RPQ + ∠RQP

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