Question

please anser this question​

Answer 1

Question :-

AD is a straight line , OB bisects ∠ AOC , if ∠ DOC = 40° then ∠ AOB = ?

a) 60°  b) 70°  c) 140°  d) 80°

$\setlength{\unitlength}{1cm}\begin{picture}(6,4)\thicklines\put(0,0){\line(1,0){5}}\put(2.5,0){\vector(-1,1){2.5}}\put(2.5,0){\vector(1,1){2.5}}\qbezier(1.8,0)(2.5,0.8)(3.2,0)\put(3.2,.3){ 40^{\circ} }\put(0.5,0){\circle*{0.15}}\put(4.5,0){\circle*{0.15}}\put(0.5,-0.5){A} \put(4.5,-0.5){D}\put(0.47,2){\circle*{0.15}}\put(0.47,2.2){B}\put(4.53,2){\circle*{0.15}}\put(4.3,2.2){C}\put(2.4,-0.4){O}\end{picture}$

Solution :-

$\rule{200}1$

∵ OB bisect ∠ AOC

∴  ∠ AOB =  ∠ BOC

$\rule{200}1$

∵ AD is a line

∴ ∠ AOB + ∠ BOC + ∠ COD = 180°

It can be written as

→  ∠ AOB + ∠ AOB + ∠ COD = 180°

→ 2 ∠ AOB + 40° = 180°

→ 2 ∠ AOB = 140°

$\dagger\underline{\boxed{\sf{\angle AOB = 70^{\circ}}}}$

Hence , option (b) 70° is correct .

$\rule{200}1$

❃Terms related to Lines and Angles

Line segment : A line segment is a part of line with two end points. a line segment has a fixed length.

Ray : A ray is a part of line which has a starting point and extends infinitely in one direction.

Perpendicular lines : two lines are said to be perpendicular when they form right angles with each other, by meeting at a single point.

Parallel lines : Two lines are said to be parallel when they do not meet at any point in a plane.

Transversal lines : When a line intersects two lines at distinct points, it is called transversal.

Acute angle : when the angle subtended by two inclinations is less than right angle then it is called an acute angle.

Obtuse angle : If the inclination b/w two arms is more than 90° , it is called obtuse angle.

Right angle : If arms form an angle 90° b/w them then it is called right angle.

Straight angle : If the arms form an angle of 180° b/w then, it is called a straight angle.

Complementary angles : Two angles which sum up to 90 degrees are called complementary angles.

Supplementary angles : Two angles which sum up to 180 degrees are called supplementary angles.

Adjacent angles : two angles having a common side and a common vertex are called adjacent angles.

Vertically opposite angles : Two angles which are formed, opposite to each other when two lines intersect at a common point, are called vertically oppostie angles.

Reflex angle : An angle that is greater than 180° and less than 360° is called a reflex angle.

Linear pair : If two adjacent angles add up to 180° they form a linear pair of angles and, these angles will form a line.

If two parallel lines are intersected by a transversal then :

• It's vertically opposite angles are equal.
• its corresponding angles are always equal.
• it's alternate interior interior and exterior angles are equal.
• Angles on the same side of transversal will be supplementary.

Answer 2

Answer:

B) 70° is your answer friend

Step-by-step explanation:

Hope it helps you friend...☺