Question

(1) If two angles of a quadrilateral measure 75° each and a third measures 60°, what is the measure of the fourth angle?

(2) Look at the figure below and answer the following questions:



(i) Write the 3 − letter names of all four angles of the quadrilateral.
(ii) In which part of the quadrilateral is the point Q located?
(iii) Which are the sides adjacent to side AD?
(iv) Which point is inside the quadrilateral?

Answer 1

(1) First angle of the quadrilateral = 75°
Second angle of the quadrilateral = 75°
Third angle of the quadrilateral = 60°
Let the fourth angle of the quadrilateral be x.
We know that sum of the angles of a quadrilateral is 360°.
∴ First angle + Second angle + Third angle + Fourth angle = 360°
⇒ 75° + 75° + 60° + x = 360°
⇒ 210° + x = 360°
⇒ x = 360° - 210°
⇒ x = 150°

(2) (i) Names of the four angles of the quadrilateral are $\angle ABC,\angle BCD,\angle CDA,\angle DAB$.
(ii) Point Q is on the exterior of the quadrilateral.
(iii) Sides adjacent to side AD are side AB and side DC.
(iv) Point P is in interior of the quadrilateral.