Name: Finding Area of Regular Polygon
Uploaded: 2019-07-19
Duration: 5 min 17 s
Description: Have you ever observed the surface of a football? The shapes on it are either regular pentagons or hexagons. The area of these polygons can be found without...

Question

Two angles of a triangle are $40 °$ and $60 °$ .Calculate all its outer angles.

Accepted Answer

Given:

In $∆ A B C$ , using angle sum property,

$∠ A + ∠ B + ∠ C = 180 °$ (Sum of the angles of triangle $= 180 °$ )

$\Rightarrow 60 ° + 40 ° + ∠ C = 180 °$

$\Rightarrow 100 ° + ∠ C = 180 °$

$\Rightarrow ∠ C = 180 ° - 100 °$

$\Rightarrow ∠ C = 80 °$

We know that, the inner angle and outer angle at each vertex form a linear pair.

Since, $∠ A C J$ and $∠ C$ are exterior and interior angles at vertex $C$ .

$∠ A C J + ∠ C = 180 °$

$\Rightarrow ∠ A C J = 100 °$

Since, $∠ C B I$ and $∠ B$ are exterior and interior angles at vertex $B$

$∠ C B I + ∠ B = 180 °$

$\Rightarrow ∠ C B I = 140 °$

Since $∠ B A H$ and $∠ B A C$ are exterior and interior angles at vertex $A$

$∠ B A H + ∠ A = 180 °$ (linear pair of angles at a vertex.)

$\Rightarrow ∠ B A H + 60 ° = 180 °$

$\Rightarrow ∠ B A H = 120 °$

Hence, the measure of the angle is $100 °, 140 °, 120 °$ .

Kerala Board Solutions for Chapter: Polygons, Exercise 2: Exercise 2

Kerala Board Mathematics Solutions for Exercise - Kerala Board Solutions for Chapter: Polygons, Exercise 2: Exercise 2

Questions from Kerala Board Solutions for Chapter: Polygons, Exercise 2: Exercise 2 with Hints & Solutions

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