Question

Find the value of x in the following diagram given that the horizontal lines are parallel to each other:
[4 MARKS]

Answer 1

Properties: 2 Marks
Steps: 1 Marks
Result: 1 Mark

In the given triangle,
Two sides are equal and the angle made by joining them is 90${}^o$.
Let the other angles be y ($\because$ equal sides have equal angles opposite to them)
For the given triangle,
Sum of all angles = 180${}^o$
Or, y + y + 90${}^o$ = 180${}^o$
Or, 2y = 180${}^o$ - 90${}^o$
Or, y = $\frac{{90}^o}{2}$ = 45${}^o$

$\because$ The two horizontal lines are parallel to each other.
$\therefore$ X = 45${}^o$ + y ($\because$ interior alternate angles are equal)
Or, X = 45${}^o$ + 45${}^o$ = 90${}^o$