Question
In figure, A, B, C, D are four points on the circle. AC and BD intersect at a point E such that $\angle$BEC = 130° and $\angle$ECD = 20° Find $\angle$BAC.
✓
Answer
Given: $\angle$BEC = 130° and $\angle$ECD = 20°
$\angle$DEC = 180° - $\angle$BEC = 180° - 130° = 50° [Linear pair]
Now in $\triangle$DEC,
$\angle$DEC + $\angle$DCE + $\angle$EDC = 180° [Angle sum property]
$\Rightarrow$ 50° + 20° + $\angle$EDC = 180° $\Rightarrow$ $\angle$EDC = 110°
$\Rightarrow$ $\angle$BAC = $\angle$EDC = 110° [Angles in same segment]
$\angle$DEC = 180° - $\angle$BEC = 180° - 130° = 50° [Linear pair]
Now in $\triangle$DEC,
$\angle$DEC + $\angle$DCE + $\angle$EDC = 180° [Angle sum property]
$\Rightarrow$ 50° + 20° + $\angle$EDC = 180° $\Rightarrow$ $\angle$EDC = 110°
$\Rightarrow$ $\angle$BAC = $\angle$EDC = 110° [Angles in same segment]
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Write the equation of the line that is parallel to x-axis and passing through the point:
(2, -5)
(2, -5)
AD and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB (See figure)
Find the measure of each angle of an equilateral triangle.
Find the zeroes of the polynomial in following:
p(x) = x - 4
p(x) = x - 4
Which of the following expressions are polynomials? In case of a polynomial, write its degree.
$2\text{x}^3+3\text{x}^2+\sqrt{\text{x}}-1$
→$2\text{x}^3+3\text{x}^2+\sqrt{\text{x}}-1$
Factorise: $6x^2 + 7x - 3$
→Find two irrational numbers between 0.16 and 0.17.
Find the curved surface area of a right circular cone whose slant height is $10 \ cm$ and base radius is $7 \ cm.$
→See Fig. and write the coordinates of the point M.
Which of the following expressions are polynomials? In case of a polynomial, write its degree.
$\text{t}^2-\frac{2}{5}\text{t}+\sqrt{5}$
→$\text{t}^2-\frac{2}{5}\text{t}+\sqrt{5}$