Mathematics

Problem

Two straight lines intersect at point

O

. One of the angles is

(4a - 15)^{\circ}

. The angle vertically opposite to it is

(2b + 25)^{\circ}

. One of the angles adjacent to

(4a - 15)^{\circ}

(b + 35)^{\circ}

. a. (i) Find the values of

a

and

b

. b. (ii) Hence, find the measure of each of the four angles at

O

Intuitive explanation

Vertical angles are always equal, and adjacent angles on a straight line always sum to $180°$ . Here you have two equations hiding in the geometry: one from the vertical angle relationship, and one from the supplementary angle relationship. Solve this system to find $a$ and $b$ , then you can determine any angle at the intersection.

Intuitive explanation

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