In the given figure, , =115^ and =70^ . Find 1. 2. 3. 4. - Vidyadip

Question

In the given figure, $\triangle\text{ODC}\sim\triangle\text{OBA},\angle\text{BOC}=115^\circ$ and $\angle\text{CDO}=70^\circ.$
Find

$\angle\text{DOC}$
$\angle\text{DCO}$
$\angle\text{OAB}$
$\angle\text{OBA}$

✓

Answer

$\triangle\text{ODC}\sim\triangle\text{OBC}$
$\angle\text{BOC}=115^\circ$
$\angle\text{CDO}=70^\circ$

$\angle\text{DOC}=(180^\circ-\angle\text{BOC})$

$=(180^\circ-115^\circ)$

$=65^\circ$

$\angle\text{OCD}=180^\circ-\angle\text{CDO}-\angle\text{DOC}$

$\angle\text{OCD}=180^\circ-(70^\circ+65^\circ)$

$=45^\circ$

Now, $\triangle\text{ABO}\sim\triangle\text{ODC}$

$\angle\text{AOB}=\angle\text{OCD }(\text{vert.Opp }\angle\text{s})=45^\circ$

$\angle\text{OAB}=\angle\text{OCD}=45^\circ$

$\angle\text{OBA}=\angle\text{ODC}$ (alternate angles) = 70º

So, $\angle\text{OAB}=45^\circ$ and $\angle\text{OBA}=70^\circ$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Triangles→Triangles — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

Which point on y-axis is equidistant from $(2, 3)$ and $(-4, 1)?$

In a given figure $, AB$ is a chord of length $8 \ cm$ of a circle of radius $5 \ cm$. The tangents to the circle at $A$ and $B$ intersect at $P$. Find the length of $AP$.

A rectangular water tank of base 11m × 6m contains water upto a height of 5m. If the water in the tank is transferred to a cylindrical tank of radius 3.5m, find the height of the water level in the tank.

In the figure below, from a cuboidal solid metallic block, of dimensions $15 cm \times 10 cm \times 5 cm$, a cylindrical hole of diameter 7 cm is drilled out. Find the surface area of the remaining block.$\left[\right.$ Use $\left.\pi=\frac{22}{7}\right]$

Use elimination method to find all possible solutions of the following pair of linear equations $a x+b y-a+b=0$ and $bx - ay - a - b =0$

If $\alpha$ and $\beta$ are zeroes of a polynomial $6 x^2-5 x +1$ then form a quadratic polynomial whose zeroes are $\alpha^2$ and $\beta^2$.

The radius of a circle with centre O Is 7cm. Two radii OA and OB are drawn at right angles to each other find the area of minor and major segments. $\Big[\text{Use }\pi=\frac{22}{7}\Big]$

Find the value of k for which the following system of equations has no solution:

$2x - ky + 3 = 0$

$3x + 2y - 1 = 0$

Show that the sum of all odd integers between $1$ and $1000$ which are divisible by $3$ is $83667.$

Evaluate the following:
If A = 60° and B = 30°, verify that:
$\sin(\text{A}+\text{B})=\sin\text{A}\cos\text{B}+\cos\text{A}\sin\text{B}$