Question:
ΔODC ~ΔOBA, \(\angle\)BOC = 125° and \(\angle\)CDO = 70°. Find \(\angle\)DOC, \(\angle\)DCO and \(\angle\)OAB.
ΔODC ~ΔOBA, \(\angle\)BOC = 125° and \(\angle\)CDO = 70°. Find \(\angle\)DOC, \(\angle\)DCO and \(\angle\)OAB.
Updated On: Nov 2, 2023
Hide Solution
Verified By Collegedunia
Solution and Explanation
DOB is a straight line.
∴ \(\angle\)DOC + \(\angle\)COB = 180°
⇒ \(\angle\)DOC = 180° − 125° = 55°
In ∆DOC,
\(\angle\)DCO + \(\angle\)CDO + \(\angle\)DOC = 180° (The sum of the measures of the angles of a triangle is 180°)
⇒ \(\angle\)DCO + 70º + 55º = 180°
⇒ \(\angle\)DCO = 55°
It is given that ∆ODC ∼ ∆OBA.
∴ \(\angle\)OAB = \(\angle\)OCD [Corresponding angles are equal in similar triangles]
⇒ \(\angle\)OAB = 55°
Was this answer helpful?
0
0
Top Questions on Triangles
- Sides $AB$ and $BC$ and median $AD$ of a $△ABC$ are respectively proportional to sides $PQ$ and $PR$ and median $PM$ of $△PQR$. Show that $△ABC ∼ △PQR$.
- If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio.
- \(D\) is a point on the side \(BC\) of \(\triangle ABC\) such that \(\angle ADC = \angle BAC\). Show that:
\(AC^2 = BC \times DC\)
- Sides $AB$ and $BC$ and median $AD$ of a $△ABC$ are respectively proportional to sides $PQ$ and $PR$ and median $PM$ of $△PQR$. Show that $△ABC ∼ △PQR$.
- If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio.
View More Questions
Questions Asked in CBSE X exam
- Both the stories ‘Two Gentlemen of Verona’ and ‘The Letter’ teach us not to lose hope and courage even in adverse situations. Write a letter to a friend justifying the statement with reference to the stories.
- CBSE Class X - 2024
- Two Gentlemen of Verona
- Et tu, Brute!’ These were the last words of Julius Caesar. Elucidate with reference to the drama ‘Julius Caesar’. Why did Caesar say these words before his death?
(Julius Caesar)- CBSE Class X - 2024
- Julius Caesar
- Humour plays a major role in the chapter, ‘Mrs. Packletide’s Tiger’. Prove this statement with the instances of humour.
(Mrs. Packletide’s Tiger)- CBSE Class X - 2024
- Mrs. Packletide's Tiger
- In the poems ‘Ozymandias’ by Percy Bysshe Shelley and ‘Not Marble, Nor the Gilded Monuments’ by William Shakespeare, the concept of Time is explored, but each poet treats it in a distinct manner. Elucidate.
- CBSE Class X - 2024
- Not Marble, Nor the Gilded Monuments
- You can feel other’s pain only when you go through it yourself. Validate this statement with reference to the story, ‘The Letter’ and why it took place?
(The Letter)- CBSE Class X - 2024
- The Letter
View More Questions