In triangle \(ABC\), angle \(ABC = 68^\circ\) and angle \(BCA = 44^\circ\). (a) Work out the size of angle \(BAC\). [2] (b) The side \(AB\) is produced to \...
Question 1 Report
In triangle \(ABC\), angle \(ABC = 68^\circ\) and angle \(BCA = 44^\circ\).
(a) Work out the size of angle \(BAC\). [2]
(b) The side \(AB\) is produced to \(D\). Work out the size of angle \(CBD\). [2]
(c) Write down the sum of the three exterior angles of triangle \(ABC\). [1]
Answer Details
This question tests the angle sum of a triangle and the exterior angle formed when a side is extended.
(a) The three angles of triangle \(ABC\) sum to \(180^\circ\), so angle \(BAC = 180 - (68 + 44)\) [M1], giving \(68^\circ\) [A1].
(b) Producing \(AB\) to \(D\) creates a straight line through \(B\), so angle \(ABC\) and angle \(CBD\) lie on a straight line and sum to \(180^\circ\). Hence angle \(CBD = 180 - 68\) [M1], giving \(112^\circ\) [A1]. (Equivalently, this exterior angle equals the sum of the two opposite interior angles, \(44 + 68 = 112^\circ\).)
(c) The exterior angles of any polygon, including a triangle, always sum to \(360^\circ\) [B1], regardless of the triangle's individual angles.
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