Question

Find the value of x in the below diagram given that, $\angle ACB$ = 25${}^o$, $\angle CBA$ = 15${}^o$ and CD is the height of C from the extended line segment BA: [4 MARKS]

Answer 1

Properties : 1.5 Marks
Steps : 1.5 Marks
Result : 1 Mark

In the given triangle ABC,
Sum of all angles of a triangle = 180${}^o$
Or, $\angle CAB$ + $\angle ABC$ + $\angle BCA$ = 180${}^o$
Or, $\angle CAB$ + 15${}^o$ + 25${}^o$ = 180${}^o$
Or, $\angle CAB$ = 180${}^o$ - 40${}^o$ = 140${}^o$

For the triangle ACD,
$\angle D$ + X = $\angle CAB$ ($\because$ sum of interior angles = exterior angle)
90${}^o$ + X = 140${}^o$ ($\because$ CD is an altitude from C to extended BA, $\therefore$ $\angle D$ = 90${}^o$)
Or, X = 50${}^o$