the figure shows square a regular pentagon and a regular hexagon put together. how much is angle BAC
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Answer:
We know that, all angles of square are 90°.
In regular pentagon,
Sum of the angles of n-sided polygon = (n – 2) × 180°
⇒ S = (5 – 2) × 180°
⇒ S = 3 × 180°
⇒ S = 540°
Measure of each interior angle
⇒ Sum of all interior angle divided by number of side
= 540°/5 = 108°
In regular hexagon,
Sum of the angles of n-sided polygon = (n – 2) × 180°
⇒ S = (6 – 2) × 180°
⇒ S = 4 × 180°
⇒ S = 720°
Measure of each interior angle
⇒ Sum of all interior angle divided by number of side
= 720°/6 =120
Let us assume the point opposite
∠ PQS + ∠ RQS + ∠ PQR = 360° (pair of angles at a vertex)
⇒ 120° + 108° + ∠ PQR = 360°
⇒ 228° + ∠ PQR = 360°
⇒ ∠ PQR = 360° - 228°
⇒ ∠ PQR = 132°
Step-by-step explanation:
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