194k views
20 votes
Hi Guys...Can Anyone Please Help With Answers and Reasons?​

Hi Guys...Can Anyone Please Help With Answers and Reasons?​-example-1
User Shalo
by
8.5k points

1 Answer

8 votes

Answer:

1. a = 64°, b = 296°, c = 148°

2. a = 90°, b = 32°, c = 58°, d = 58°, e = 29°, f = 29°, g = 29°, h = 29°, i = 122°, j = 122°

3. a = 35°, b = 35°, c = 70°, d = 35°, e = 35°, f = 110°, g = 22°

4. a = 27°, b = 63°, c = 27°, d = 54°, e = 90°, f = 36°, g = 63°

5. t = 40°, u = 40°, v = 80°, w = 21°, x = 42°, y = 19°, z = 19°

Explanation:

On the same arc angle subtended at center is twice the angle subtended at circumference

same arc, same angle on any point on the circumference

1.

a = 2 * 32° = 64°

b = 360° - a = 360° - 64° = 296°

c = b/2 = 296°/2 = 148°

a = 64°, b = 296°, c = 148°

2.

a = 180 - 90 = 90°

triangle OMT and triangle ONT are congruent

b = 32°

c = 90 - 32 = 58°

d = c = 58°

f = c /2 = 58/2 = 29°

exterior angle, c = h + f

h = c - f = 58 - 29 = 29°

j = 180 - c = 180 - 58 = 122°

similarly, e = g = 29°, i = 122°

a = 90°, b = 32°, c = 58°, d = 58°, e = 29°, f = 29°, g = 29°, h = 29°, i = 122°, j = 122°

3.

a = 70/2 = 35°

As TR = VT, b = a = 35°

arc VTR, c = a + b = 35° + 35° = 70°

arc VT, d = a = 35°

TR = VT, e = d = 35°

cyclic quadrilateral, f + a + b = 180, f = 180 - a - b = 180 - 35 - 35 = 110°

arc PQ, g = angle PRQ = 22°

a = 35°, b = 35°, c = 70°, d = 35°, e = 35°, f = 110°, g = 22°

4.

arc PQ, a = 27°

b = 90 - 27 = 63°

MP is diameter, b + c = 90°, c = 90 - b = 90 - 63 = 27°

g = 90 - c = 90 - 27 = 63°

e = 180 - 90 = 90°

angle NPR = 90 - 27 = 63°

ON + OP, a + f = angle NPR = 63°, f = 63 - a = 63 - 27 = 36°

d = 90 - f = 90 - 36 = 54°

a = 27°, b = 63°, c = 27°, d = 54°, e = 90°, f = 36°, g = 63°

5.

arc BC, t = u = 40°

arc AB, w = 21°

arc BC, v = 2u = 2 * 40 = 80°

arc AB, x = 2 * 21 = 42°

OA = OC, y = z = ( 180 - x - v )/2 = ( 160 - 42 - 80 )/2 = 19°

t = 40°, u = 40°, v = 80°, w = 21°, x = 42°, y = 19°, z = 19°

User Raktotpal Bordoloi
by
7.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories