AC←→ is tangent to the circle with center at B. The measure of ∠ACB is 24°. What is the measure of ∠ABC?

enter image source here

2 Answers
Mar 10, 2017

Answer:

#66^@#

Explanation:

Given that #AC# is tangent to the circle and #B# is the center of the circle,
#=> angleCAB=90^@#
Given #angleACB=24^@#,
#=>angleABC=180-angleCAB-angleACB#
#=180-90-24=66^@#

Mar 11, 2017

Answer:

#66^circ#

Explanation:

enter image source here

Now we know that #angleCAB=90^circ# and #angleACB=24^circ#

Our goal is to find the third angle, so we use the property:

#color(brown)("Sum of the three angles of a triangle is"# #color(brown)(180^circ#

So,

#rarrangleCAB+angleACB+angleABC=180^circ#

#rarr90^circ+24^circ+angleABC=180^circ#

#rarr114^circ+angleABC=180^circ#

#rarrangleABC=180^circ-114^circ#

#color(green)(rArrangleABC=66^circ#

Hpe this helps..... :)