Advertisements
Advertisements
Question
Two lines AB and CD intersect at O. If ∠AOC + ∠COB + ∠BOD = 270°, then ∠AOC =
Options
70°
80°
90°
180°
Advertisements
Solution
Let us draw the following diagram showing two lines AB and CD intersecting at a point O.
Thus, ∠AOC, ∠COB, ∠AODand ∠BODform a complete angle, that is the sum of these four angle is 360°.
That is,
∠AOC + ∠COB +∠BOD+ ∠AOD = 360° (I)
It is given that
∠AOC + ∠COB + ∠BOD = 270° (II)
Subtracting (II) from (I), we get:
∠AOD = 360° - 270°
∠AOD = 90°
If one of the four angles formed by two intersecting lines is a right angle, then each of the four angles will be a right angle.
So, ∠AOC = \[90^\circ\]
APPEARS IN
RELATED QUESTIONS
In the below fig, lines �1 and �2 intersect at O, forming angles as shown in the figure. If x = 45, Find the values of x, y, z and u.
In the below fig, rays AB and CD intersect at O.
Determine y when x = 60°
In the below fig, lines AB, CD and EF intersect at O. Find the measures of ∠AOC, ∠COF,
∠DOE and ∠BOF.
Two lines AB and CD intersect at O. If `∠`AOC + `∠`COB + `∠`BOD = 270°, find the
measures of `∠`AOC, `∠`COB, `∠`BOD and `∠`DOA.
If l, m, n are three lines such that l || m and n ⊥ l, prove that n ⊥ m.
Consider the following statements:
When two straight lines intersect:
(i) adjacent angles are complementary
(ii) adjacent angles are supplementary
(iii) opposite angles are equal
(iv) opposite angles are supplementary
Of these statements
In the given figure, which of the following statements must be true?
(i) a + b = d + c
(ii) a + c + e = 180°
(iii) b + f = c + e
Look at the picture given below. Decide whether the lines given in picture is parallel or perpendicular to each other and write the answer in the box.
Two lines in a plane which do not meet at a point anywhere are called ______ lines.
If the shortest distance between two straight lines in a plane is observed to change, what must be true about the lines?
