Fill in the missing angles for each with a given reason.

2. Originally Posted by sammyfox07

Fill in the missing angles for each with a given reason.

Cute problems! Q3: for example:
a = 55 b/c it's the same angle! ( // lines and they lie along the same line)

therefore.

......64
...55...(180-64-55) (180 degrees in a triangle)
55......................??....??

......64
...55...61
55........61(due to same reasoning)...??

and since angle 61 and b lie along the same line, it is complimentary and equals 180.

......64
...55...61
55........61...(180-61)

therefore

......64
...55...61
55........61...119

b = 119
a = 55

This should help for the other two problems:
Angles

For reference: f and g in Q1 equal 133 degrees.
To find f, use the fact that the angle given and f are 'adjacent angles'.
To find g, you will have to use the fact that the angle given and another angle are 'corresponding angles'. Then you will have to use 'adjacent angles' again.

For reference: AC must be the diameter of the circle in order to solve it. If AC is the diameter, then the greater triangle has angles 90, f and g.
a+b=90 (where a and b are smaller angles that compose the 90 degrees)
f+a+110=180
g+b+(180-110)=180

Solve~

3. Originally Posted by AgentNXP
Cute problems! Q3: for example:
a = 55 b/c it's the same angle! ( // lines and they lie along the same line)

therefore.

......64
...55...(180-64-55) (180 degrees in a triangle)
55......................??....??

......64
...55...61
55........61(due to same reasoning)...??

and since angle 61 and b lie along the same line, it is complimentary and equals 180.

......64
...55...61
55........61...(180-61)

therefore

......64
...55...61
55........61...119

b = 119
a = 55
or you could use the fact that (theorem) the external angle of a triangle is equal to the sum of the two opposite interior angles (this is not very hard to see if you think about it). thus immediately, we know b = 64 + 55 = 119.

for a, we have similar triangles, corresponding angles are equal, so a = 55 by inspection

4. for the first. p and 47 are supplementary (they add up to 180 degrees) since they are angles on a straight line. also, angle p = angle g, since they are alternate exterior angles