Question

The measure of angle 3 is 42°. 3 lines intersect to form 5 angles. From top left, clockwise, the angles are 2 (90 degrees), 1, 5, 4, 3. What is the measure of angle 1 in degrees?

Answer 1

Answer:

Angle 1 =  48°

Step-by-step explanation:

The total of the angles 1,5, 4, 3  is 180 degrees = 2( 90 degrees)  ( given)

So

< 1+ < 5+ <4 + < 3 = 180°

but , < 3= 42°

so  < 1 + <5 + <4 = 180° - 42° = 138°

It can deduced that <5 + <4 = 90° (***)

so <1 = 138°- 90°= 48°

(***) when we draw four angles in such a way that their sum is 180 °. Then either the sum of the first two angles is 90 ° or the sum of the second and third angle is 90 °. Similarly the third or fourth angle is 90 ° or fourth and first angle is 90 °.

The diagram is given to elaborate this point

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