Question 1: Two angles of a triangle measure . Find the measure of the third angle.

Answer:

Sum of all the angles of a triangle

Let the third angle

Therefore

Or

Question 2: Three angles of a triangle are in the ratio of . Find the angles of the triangle.

Answer:

Let the angles be

Therefore

Or

Therefore the angles are

Question 3: One angle of the triangle is and the other two angles are equal. Find the measure of each angle of the triangle.

Answer:

Let the two equal angles be

Therefore

Or

Therefore the angles are

Question 4: One angle of the triangle is and the other two angles are in the ratio . Find the measures of each of the unknown angles.

Answer:

Let the two unknown angles be

Therefore

Or

Or

Therefore the two angles are

Question 5: Three angles of a triangle measures . Find the value of and the measures of all the angles.

Answer:

Or

Hence the angles are

Question 6: In . Find the value of and the measure of all the angles of the triangle.

Answer:

or

Hence

Question 7: In . Find the value of x and the measure of all the angles of the triangle and show that the triangle is an isosceles triangle.

Answer:

Hence

Question 8: In . Find the angles of the triangle.

Answer:

Let

Question 9: In the adjoining figure, it is given that . Find the value of $latex .

Answer:

Note: Sum of angles of adjacent angles on a straight line

Note:Sum of all angles of a triangle

Question 10: In the adjoining figure, it is given that and are bisectors of respectively. Find the measure of

Answer:

Let

Since

Question 11: Using the information given in the adjoining figure, find the value of

Answer:

Question 12: In the adjoining figure, is a straight line, . Find

Answer:

Therefore

Question 13: Find, giving reasons, the unknown angles marked by in the following figures.

Answer:

i)

ii)

iii)

iv)

v)

vi)

Given which means

Question 14: In the adjoining figure, if , find the value of and hence, find the measure of

Answer:

Question 15: In , side AC has been produced to D. If , find the measure of

Answer:

Let

Therefore

Question 16: In the adjoining figure, it is given that: . Find the measure of

Answer:

i)

Note:Co-interior Angles

ii)

iii)

Question 17: In the adjoining figure, it is given that:. Find

Answer:

Therefore

i) & ii) Hence

iv)

iii)

Question 18: Using the information given in the adjoining figure, calculate the values of

Answer:

In

In

Question 19: Sides have been produced to D and E respectively. are bisectors of respectively. If , find the measure of

Answer:

Given

Question 20: In the adjoining figure, it is being given that . Find the value of .

Answer:

Note:Alternate angles

Question 21: In the adjoining figure, it is being given that . Find the value of .

Answer:

In

In

Question 22: In the adjoining figure, it is given that Find the value of

Answer:

In

In

In

Question 23: In the adjoining figure,

Answer:

In

Since

Note:Alternate Angles

Substituting ii) in i) we get

Substituting the value of

Question 24: In the adjoining figure, . Find the values of

Answer:

In

Since

Substituting ii) in i) we get

Substituting in ii) we get