Advertisements
Advertisements
Question
Find the value of x, y and z
Advertisements
Solution
∠DOB and ∠BOC are linear pair
∴ ∠DOB + ∠BOC = 180°
x + 3x + 40 = 180°
4x + 40 = 180°
4x + 40 – 40 = 180° – 40°
4x = 140°
x = `(140^circ)/4`
x = 35°
Also ∠BOD and ∠AOC are vertically opposite angles.
∴ ∠BOD = ∠AOC
x = z + 10
35° = z + 10
z + 10 – 10 = 35 – 10
z = 25°
Again ∠AOD and ∠AOC are linear pair.
∴ ∠AOD + ∠AOC = 180°
y + 30 + z + 10 = 180°
y + 30 + 25 + 10 = 180°
y + 65 = 180°
y + 65 – 65 = 180° – 65
y = 115°
∴ x = 35°,
y = 115°,
z = 25°
APPEARS IN
RELATED QUESTIONS
Indicate which pairs of angles are: Linear pairs.
There are six angles at a point. One of them is 45° and the other five angles are all equal. What is the measure of all the five angles?
In the figure POQ, ROS and TOU are straight lines. Find the x°
In the following figure, POQ is a line, then a is ______.
In the following figure, PQ || RS. If ∠1 = (2a + b)° and ∠6 = (3a – b)°, then the measure of ∠2 in terms of b is ______.
Two supplementary angles always form a linear pair.
A linear pair may have two acute angles.
In the following figure, write, if any, (i) each pair of vertically opposite angles, and (ii) each linear pair.
What is the type of other angle of a linear pair if one of its angles is right?
