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In this lesson, we will learn how to find a missing angle in a triangle given the two other angles using the triangle angle-sum theorem.

Q1:

Determine the values of and .

Q2:

The measures of the base angles of an isosceles triangle are ( 9 π β 2 π ) β and ( 5 π + 2 π ) β , and the measure of the vertex angle is ( 4 π ) β . Find the values of π and π .

Q3:

Find the size of .

Q4:

In , . If is an altitude of , find .

Q5:

If the ratio between the sizes of the angles of a triangle is , determine the sizes of the angles.

Q6:

If π΄ π΅ πΆ is a triangle in which π β π΄ = 7 9 π β π΅ and π β πΆ = 2 π β π΄ . Calculate the measures of angles π΄ , π΅ , and πΆ .

Q7:

The figure shows a rectangle π΄ π΅ πΆ π· and a square π΄ π΅ π π . What is π β π΄ π π· ?

Q8:

In triangle π΄ π΅ πΆ , π β π΄ = 7 8 β and π β π΅ = 2 π β πΆ . What is π β πΆ ?

Q9:

Complete the following: The sum of measures of the interior angles of a triangle is .

Q10:

Fady is experimenting with the interior angles of a triangle. He colours the angles, cuts them out, and sticks them together as seen in the figure. Will Angle π§ fit with Angles π₯ and π¦ to create a straight line?

Q11:

In the figure below, given that π΄ π΅ πΆ π· is a rectangle, determine π β πΆ π· πΈ .

Q12:

Q13:

In the triangle π΄ π΅ πΆ , π β π΄ = οΉ π₯ + 9 7 ο 2 β , π β π΅ = ( 6 0 β 5 π₯ ) β , and π β πΆ = ( 5 9 β 7 π₯ ) β . Find the measure of each angle.

Q14:

What is the sum of the measures of the two acute angles in a right-angled triangle?

Q15:

The sum of the measures of the angles of a triangle is 1 8 0 β . In a right triangle, what is the sum of the measures of the two acute angles?

Q16:

The given design is carved on a wooden board. If is a right angle, determine the values of , , and .

Q17:

Q18:

Given that π΄ π΅ πΆ is a triangle in which π β π΄ = ( 2 π₯ + 6 ) β , π β π΅ = ( 3 π₯ + 3 ) β , and π β πΆ = ( 5 π₯ + 6 ) β , determine π β π΄ .

Q19:

In β³ π΄ π΅ πΆ , π β π΅ = 2 π β π΄ = 4 0 β . Determine π β πΆ .

Q20:

Complete the sentence: The measure of a straight angle is the sum of the measures of the interior angles of a triangle.

Q21:

Suppose that in the figure, π β πΏ = 2 π₯ β and π β πΎ = 4 π₯ β . Determine these two angles.

Q22:

Find the measure of each angle in the triangle below.

Q23:

The hexagon in the figure has been divided into triangles. Use what you know about the angle sum of a triangle to find the angle sum of the hexagon.

Q24:

Find π β π΄ π΅ πΆ .

Q25:

The sizes of the angles in a triangle are in a ratio of . Work out the sizes of these angles.

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