Question

determine angle P + angle Q + angle R + angle S + angle T in the given figure

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Answer 1

Answer:

Step-by-step explanation:

Here ABCDE is a pentagon and each interior angles A,B,C,D,E=108

Consider quadrilateral ABQE

Sum of angles in Quadrilateral =360

108+108+108+Q=360

Q=36

Similarly all P=Q=R=S=T=36

P+Q+R+S+T=180

Answer 2

∠P + ∠Q + ∠R + ∠S + ∠T = 180°

Step-by-step explanation:

In question figure,

To find, ∠P + ∠Q + ∠R + ∠S + ∠T = 180°

We know that,

The pentagon of each interior angle = 108°

∴ ABCDE is a pentagon,

∠ A, ∠B, ∠C, ∠D and ∠E = 108 °

Consider quadrilateral ABQE ,

The sum of all angles in quadrilateral = 360 °

∴ ∠ A + ∠B + ∠C + ∠Q = 360 °

⇒ 108° + 108° + 108° + ∠Q = 360 °

⇒ ∠Q =360 °- 324° = 36°

Similarly.

All ∠P = ∠Q = ∠R = ∠S= ∠T = 36 °

∴ ∠P + ∠Q + ∠R + ∠S + ∠T = 180°