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In this lesson, we will learn how to find a missing angle's measure in a quadrilateral knowing that the sum of angles in a quadrilateral is 360 degrees.

Q1:

π΄ π΅ πΆ π· is a quadrilateral where π β π΄ = 1 6 5 β , π β π΄ π΅ πΆ = 4 π₯ β , π β π΅ πΆ π· = 4 π₯ β , and π β πΆ π· π΄ = 5 π₯ β . What is π₯ ?

Q2:

In the given figure, π β π΄ = 7 4 β and π β πΆ = 9 2 β . Find π β π· .

Q3:

Determine the value of π₯ in the given quadrilateral.

Q4:

Find .

Q5:

In a quadrilateral , if , find .

Q6:

The sum of the sizes of the angles of a trapezium is . Write an equation to find the missing size , and then solve it.

Q7:

From the figure, in which π β πΆ π· π΄ = 5 π₯ β , π β π΅ πΆ π· = 7 π¦ β , and π β π΄ π΅ πΆ = 8 π¦ β , find the values of π₯ and π¦ .

Q8:

Given that π β π· = 2 3 π β π΅ , find π β π΅ and π β π· .

Q9:

Determine π β πΆ π΄ π΅ .

Q10:

From the figure, determine π β π΅ πΈ π· .

Q11:

In the figure, π β π΄ = 3 4 β , π β πΉ = 4 8 β , and π β π΅ πΈ πΉ = 3 4 β . Determine the measure of all angles in π· πΈ π΅ πΆ .

Q12:

Determine π β πΉ πΈ πΆ .

Q13:

In the figure, if π β π΄ = 2 6 β , π β π΄ πΆ π΅ = 5 4 β , π β πΉ = 1 4 6 β , determine π β πΈ .

Q14:

The internal angles of a quadrilateral are in the ratio 3 βΆ 4 βΆ 5 βΆ 6 . What is the largest angle?

Q15:

In the given figure, find and .

Q16:

Find the sizes of the angles of a quadrilateral given that the ratio between them is .

Q17:

π΄ π΅ πΆ π· is a quadrilateral where π β π΄ = 1 6 2 β , π β π΄ π΅ πΆ = 4 π₯ β , π β π΅ πΆ π· = 2 π₯ β , and π β πΆ π· π΄ = 3 π₯ β . What is π₯ ?

Q18:

Q19:

Q20:

Q21:

Q22:

Q23:

In the given figure, π β π΄ = 6 0 β and π β πΆ = 1 1 8 β . Find π β π· .

Q24:

In the given figure, π β π΄ = 7 5 β and π β πΆ = 9 6 β . Find π β π· .

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