Question

Find the measures of angles a and b in the figure to the right. Justify your results.

Answer 1

As shown in the given triangle :

The triangle contains the angle a is also contains the angles 58 and 69

The sum of the angles of the triangle = 180

So, the measure of angle a =

$180-(58+69)=180-127=53$

So, the measure of angle a = 53

Now , for the angles 93 and 58 and the angle between them

Let the angle between the angles 93 and 58 = x

The sum of these angles = 180

So, the missing angle = x = 180 - ( 93 + 58 ) = 29

And the angle 69 is an exterior angle for the upper triangle

so, 69 = b + x

So,

$b=69-x=69-29=40$

So, the answer is :

The measure of angle a = 53

The measure of angle b = 40