The measure of ∠ABD = 67 , ∠CBD= 67 and ∠ABC = 134 .
Angles are formed when two lines intersect at a point. The measure of the 'opening' between these two rays is called an 'angle'. It is represented by the symbol ∠. Angles are usually measured in degrees and radians, which is a measure of circularity or rotation.
An angle is formed by two rays that share a common endpoint. Each ray is called a side of the angle and the common endpoint is called the vertex. An angle is named by its vertex. In the image below, ∠A is the angle with vertex at point A. The measure of ∠A is written .
Angles are a part of our day-to-day life. Engineers and architects use angles for the design of roads, buildings, and sporting facilities. m∠A.
Given :
Angle BD bisects angle ABC , which means it divides angle ABC into 2 equal parts
⇒ ∠ABD =∠ABD
12 = 3x
⇒ x = 4
∠ABD = 8x + 35
= (8 * 4) + 35
= 32 + 35
= 67
∠DBC = 11x + 23
= (11 * 4) + 23
= 44 + 23
= 67
∠ABC = ∠ABD + ∠DBC
= 67 +67
= 134
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