FINDING ANGLES IN ISOSCELES TRIANGLES WORKSHEET

Problem 1 :

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Problem 2 :

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Problem 9 :

Problem 10 :

The figure alongside has not been drawn accurately:

a) Find x.

b) What can be deduced about the triangle?

Solution

Problem 11 :

The degree measure of the vertex angle is (7x - 27).  The degree measure for each base is (9x - 34) . What is the value of one base angle?

Solution

Problem 12 :

The ratio of the measure of a base angle in an isosceles triangle to the measure of the vertex angle is 2:16. Find the measure of each angle.

Solution

Problem 13 :

The degree measure of the vertex angle is (x + 21). The degree measure for each base is (2x + 17) . What is the value of x?

Solution

Problem 14 :

The vertex angle of an isosceles triangle is 76 . The degree measure for each base . What is the measure of one base angle?

Solution

Problem 15 :

The ratio of the measure of a base angle in an isosceles triangle to the measure of the vertex angle is 1:7. Find the measure of each angle.

Solution

Problem 1 :

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Problem 2 :

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Problem 5 :

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Problem 7 :

In the figure given below, PQ = PS. The value of x is 

a)  35    b)  45     c)  55     d) 70

Solution

Problem 8 :

Find the measures of the angles of an isosceles triangle if the measure of the vertex angle is 40 degrees less than the sum of the measures of the base angles.

Solution

Problem 9 :

In an isosceles triangle, one angle is 70°. The other two angles are of

(i) 55° and 55° (ii) 70° and 40° (iii) any measure

In the given option(s) which of the above statement(s) are true?

(a) (i) only      (b) (ii) only    (c) (iii) only     (d)  (i) and (ii)

Solution

Problem 10 :

In a triangle, one angle is of 90°. Then

(i) The other two angles are of 45° each

(ii) In remaining two angles, one angle is 90° and other is 45°

(iii) Remaining two angles are complementary In the given option(s) which is true?

(a) (i) only      (b) (ii) only      (c) (iii) only     (d) (i) and (ii)

Solution

Problem 1 :

Use the diagram of ΔABC shown below to prove the Base Angles Theorem.

Solution

Problem 2 :

In the diagram shown below,

(i) find the value of x

(ii) find the value of y

Solution

Problem 3 :

In the diagram shown below,

(i) find the value of x

(ii) find the value of y

Solution

Problem 4 :

In an acute triangle, the measures of two angles are 50° and 60°. What is the measure of the third angle?

Solution

Problem 5 :

In an obtuse triangle, the measures of two angles are 120° and 10°. What is the measure of the third angle?

Solution

Problem 6 :

One acute angle of a right triangle measures 35°. What is the measure of the other acute angle?

Solution

Problem 7 :

Find the angle measures of a triangle if the second angle measures 10 degrees less than twice the first, and the third angle measures 25 degrees more than the second.

Solution

Problem 8 :

The measure of the second angle is 15 degrees more than the measure of the first angle. The measure of the third angle is 45 degrees more than the measure of the first angle. Find the measures of the interior angles in the triangle.

Solution

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