MCQ
In Fig. what is the value of $x?$
- A$35^\circ$
- B$45^\circ$
- C$50^\circ$
- ✓$60^\circ$
✓
Answer
Correct option: D.
$60^\circ$
In $\triangle\text{ABC},$
$\angle\text{BCA}+\angle\text{CAB}+\angle\text{ABC}=180^\circ$
$\Rightarrow3\text{y}^\circ+\text{x}^\circ+5\text{y}^\circ=180^\circ$
$\Rightarrow8\text{y}^\circ+\text{x}^\circ=180^\circ\dots(1)$
Also, $5\text{y}^\circ=180^\circ-7\text{y}^\circ$
$\Rightarrow12\text{y}^\circ=180^\circ$
$\Rightarrow\text{y}^\circ=15^\circ$
From (1), $\text{x}^\circ=180^\circ-8\text{y}^\circ$
$\Rightarrow\text{x}^\circ=180^\circ-8\times15^\circ$
$\Rightarrow\text{x}^\circ=60^\circ$
$\angle\text{BCA}+\angle\text{CAB}+\angle\text{ABC}=180^\circ$
$\Rightarrow3\text{y}^\circ+\text{x}^\circ+5\text{y}^\circ=180^\circ$
$\Rightarrow8\text{y}^\circ+\text{x}^\circ=180^\circ\dots(1)$
Also, $5\text{y}^\circ=180^\circ-7\text{y}^\circ$
$\Rightarrow12\text{y}^\circ=180^\circ$
$\Rightarrow\text{y}^\circ=15^\circ$
From (1), $\text{x}^\circ=180^\circ-8\text{y}^\circ$
$\Rightarrow\text{x}^\circ=180^\circ-8\times15^\circ$
$\Rightarrow\text{x}^\circ=60^\circ$
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
Area of a right-angled triangle is $6 cm^2$ and its perimeter is 12 cm. Then length of its hypotenuse, is
→In the given figure, $AB \| CD \| EF,$ $\text{EA }\bot\text{ AB}$ and BDE is the transversal such that $\angle\text{DEF}=55^\circ,$ Then $\angle\text{AEB}=?$
→Write the correct answer in the following: After rationalising the denominator of $\frac{7}{3\sqrt{3}-2\sqrt{2}},$ we get the denominator as
→→
A chord is at a distance of $8\ cm$ from the centre of a circle of radius $17\ cm.$ The length of the chord is:
→Two adjacent sides of a parallelogram are $74\ cm$ and $40\ cm$ and one of its diagonals is $102\ cm.$ Area of the parallelogram is:
→In the above quadrilateral $ACBD$, we have $AC= AD$ and $AB$ bisect the $LA$ .Which of the following is true?
→$ABC$ is an isosceles triangle such that $AB = AC$ and $AD$ is the median to base BC. Then, $\angle\text{BAD}=$
→A circle is drawn. It divides the plane into:
In the given figure, $CD$ is the diameter of a circle with centre $O$ and $CD$ is perpendicular to chord $AB.$ If $AB = 12\ cm$ and $CE = 3\ cm,$ then radius of the circles is:
→