Question

<1 is in a triangle work <4 and a 53° angle . what is the sum of the measures of these two angles

Answer 1

In the small triangle

There are a right angle and an acute angle of measure 53 degrees

Since the sum of the angles of a triangle is 180 degrees

Then 90 + 53 + < 1 = 180 degrees

Then 143 + < 1 = 180

Subtract 143 from both sides

Then < 1 = 37 degrees

Since <2 is an exterior angle of the small triangle

Then its measure = the sum of <1 and 90 degrees

Then < 2 = 37 + 90 = 127 degrees

In the triangle of angles 2, n3 and 30

< 2 + < 3 + 30 = 180

127 + < 3 + 30 = 180

Add 127 and 30

157 + <3 = 180

<3 = 23

The answer is < 2 = 127 degrees and < 3 = 23 degrees