Question

in triangle abc, if an exterior angle drawn at vertex c measures 45, then angle b... A. must be acute B. must be a right angle C. must be an obtuse angle D. may be either an obtuse or acute angle

Answer 1

Angle 45 = Angle x + Angle a

Answer 2

(the triangle i made is not to scale)

\[45 > x\]
\[45 > a\]
Which means Angle "x" cannot be greater than 45 and an Obtuse angle is greater than 90.
Acute Angle is smaller than 90 so 45 comes in the range of 90. And if the angle "x" was a Right-Angle then it means it would be 90, but it would be greater than 45 so we would say angle "x" is an Obtuse angle.

Answer is "C". Must be an Obtuse angle.

Answer 3

or
angle c = 180 - 45 =
and if angle c is obtuse (greater than 90 degrees)
then you can use the rule that a triangle can only have one obtuse angle
and so the other angles would have to be acute.

Answer 4

thanks

Answer 5

you're welcome :)

Answer 6

You need to learn the Theorem,
"An measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles."



Angle 4 = Angle 2 + Angle 3

And also:

Angle 4 is greater than Angle 2 & Angle 4 is greater than Angle 3

Answer 7

You're Welcome! :)