Question

In the given figure , two of the angles are indicated . What are the measures of ACX and

ACB. ​

Answer 1

$\pink{Exterior \: Angle \: Theorem}$

An exterior angle of a triangle is equal to the sum of the two remote (nonadjacent) interior angles.

$angle \: bac + angle \: abc\: = angle \:a cx$

$60 \: °+ 75 \:°$

$135 \: °$

$angle \: acx = 135 \: °$

$\pink{linear \: pair\: Theorem}$

when two angles are formed on the same line segment and are almost joined by a line or angle bi sector then their sum is 180 °

$angle \: acb \: = 180° - 135° = 45°$

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