please answer this question step by step
Answers
Answer:
→For First Polygon
- a=100°
- b=30°
- c=90°
- d=110°
- e=30°
→ For Second polygon
- x=70°
- y=95°
- w=105°
- z=90°
Step-by-step explanation:
To solve this question we need to know 2 things
- The sum of interior angles for n-sided polygon=(n-2)×180°
- The sum of interior and exterior angle at a vertex is always 180°
→So now taking the first figure
We need to find the interior angle at E.
Since it is a 5 sided polygon, the sum of interior angles=(5-2)×180°=3×180°=540°
∴80°+150°+90°+70°+∠E=540°
⇒390°+∠E=540°
⇒∠E=540°-390°
⇒∠E=150°
At vertex A
∠a+80°=180° ∵interior angle+exterior angle=180°
⇒∠a=180°-80°
⇒∠a=100°
At Vertex B
∠b+150°=180° ∵interior angle+exterior angle=180°
⇒∠b=180°-150°
⇒∠b=30°
At Vertex C
∠c+90°=180° ∵Interior angle at C is 90°(from figure)
⇒∠c=180°-90° ∵interior angle+exterior angle=180°
⇒∠c=90°
At Vertex D
∠d+70°=180° ∵interior angle+exterior angle=180°
⇒∠d=180°-70°
⇒∠d=110°
At Vertex E
∠E+∠e=180° ∵interior angle+exterior angle=180°
⇒∠e=180°-150° ∵∠E=150° as we found earlier
⇒∠e=30°
→ For Second figure
first let us calculate the interior angle at D
As we know,
sum of interior angles for n-sided polygon=(n-2)×180°
⇒85°+90°+110°+∠A=(4-2)×180°
⇒285°+∠A=2×180°
⇒∠A=360°-285°
⇒∠A=75°
At Vertex A
∠A+∠w=180° ∵interior angle+exterior angle=180°
⇒∠w=180°-75°
⇒∠w=105°
At Vertex B
85°+∠y=180° ∵interior angle+exterior angle=180°
⇒∠y=180°-85°
⇒∠y=95°
At Vertex C
90°+∠z=180° ∵interior angle+exterior angle=180°
⇒∠z=180°-90°
⇒∠z=90°
At Vertex D
110°+∠x=180° ∵interior angle+exterior angle=180°
⇒∠x=180°-110°
⇒∠x=70°