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

Compute all angles in the figure below.

Accepted Answer

We know that, the interior angle and exterior angle at each vertex form a linear pair.

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

$∠ C B I + ∠ B = 180 °$

$\Rightarrow 105 ° + ∠ B = 180 °$

$\Rightarrow ∠ B = 75 °$

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

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

$\Rightarrow ∠ B A H + 35 ° = 180 °$

$\Rightarrow ∠ B A H = 180 ° - 35 °$

$\Rightarrow ∠ B A H = 145 °$

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

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

$\Rightarrow 35 ° + 75 ° + ∠ C = 180 °$

$\Rightarrow 110 ° + ∠ C = 180 °$

$\Rightarrow ∠ C = 70 °$

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

$∠ C + ∠ A C J = 180 °$ (linear pair of angles at a vertex)

$\Rightarrow 70 ° + ∠ A C J = 180 °$

$\Rightarrow ∠ A C J = 180 ° - 70 °$

$\Rightarrow ∠ A C J = 110 °$

Hence, the measure of the exterior angles are $145 °$ and $110 °$ , interior angles are $75 °$ and $70 °$

Compute all angles in the figure below.

Important Questions on Polygons

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