angle A minus angle C is equal to 35 degree is equal to 85 degree and B equal to what and C is equal to what
Answers
Answer:
Q3. What is the sum of the measures of the angles of a convex quadrilateral? Why this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)
Ans. Angle sum of a convex quadrilateral = (4 – 2) × 180° = 2 × 180° = 360°
Since, quadrilateral, which is not convex, i.e. concave has same number of sides i.e. 4 as a convex quadrilateral have, thus, a quadrilateral which is not convex also hold this property. i.e. angle sum of a concave quadrilateral is also equal to 360°
Q4. Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)
What can you say about the angle sum of a convex polygon with number of sides?
(a) 7
Ans. Given number of sides = 7
Angle sum of a polygon with 7 sides
= (7 – 2) × 180° = 5 × 180° = 900°
(b) 8
Ans. Given number of sides = 8
Angle sum of a polygon with 8 sides
= (8 – 2) × 180° = 6 × 180° = 1080°
(c) 10
Ans. Given number of sides = 10
Angle sum of a polygon with 10 sides
= (10 – 2) × 180° = 8 × 180° = 1440°
(d) n
Ans. Given number of sides = 7
Angle sum of a polygon with n sides = (n – 2) × 180° = (n – 2)180°
Q5. What is a regular polygon?
State the name of a regular polygon of
(i) 3 sides (ii) 4 sides
(iii) 6 sides
Ans. A polygon with equal sides and equal angles is called reagular polygon.
(i) Equilateral triangle
(ii) Square
(iii) Regular hexagon
Q6. (a) Find the angle measures x in the following figures.
Ans. We know that, angle sum of a quadrilateral = 360°
∴ 50° + 130° + 120° + x = 360°
⇒ 300° + x = 360°
⇒ x = 360° – 300°
⇒ x = 60° Answer
Q6. (b)
Ans. We know that, angle sum of a quadrilateral = 360°
∴ 90° + 60° + 70° + x = 360°
⇒ 220° + x = 360°
⇒ x = 360° – 220°
⇒ x = 140° Amswer
Q6. (c)
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