Question

give the statements and the reasons . AB//TC,C=65 and C=43 calculate the size of A,B1 and B2

Answer 1

[AI-generated answer — Bot GPT 3.5]

Statements:

1. AB is parallel to TC (AB//TC)
2. The measure of angle C is 65 (C = 65)
3. The measure of angle C is 43 (C = 43)

Reasons:
1. AB is parallel to TC: This statement is given.
2. The measure of angle C is 65: This is a given statement.
3. The measure of angle C is 43: This is a given statement.

Calculations:
Since AB is parallel to TC, the alternate interior angles are congruent. Therefore, angle A is also 65 degrees (corresponding angles).
Similarly, since AB is parallel to TC, the alternate interior angles are congruent. Therefore, angle B1 is also equal to angle C, which is 43 degrees.
Now, to find angle B2, we can use the fact that the sum of angles in a triangle is 180 degrees. Since we already know angle A and angle B1, we can subtract their measures from 180 to find angle B2.
Angle B2 = 180 - angle A - angle B1
Angle B2 = 180 - 65 - 43
Angle B2 = 72 degrees

Therefore,
Size of angle A = 65 degrees
Size of angle B1 = 43 degrees
Size of angle B2 = 72 degrees