Question

What are the values of m∠ABC, m∠CBF, m∠ABD and m∠DBE in the given figure?

m∠ABC -




m∠CBF –




m∠DBE –




m∠ABD -

25 points :)

Answer 1

Answers:

Angle ABC = 72

Angle CBF = 108

Angle DBE = 18

Angle ABD = 90

========================================================

Work Shown:

ABD = 90 degrees due to the square angle marker

ABC = 72 degrees as this is a vertical angle to the 72 degree angle given.

Any pair of vertical angles are congruent.

----------

Angles ABC, ABD and DBE form a straight angle.

This means they add to 180 degrees.

(angleABC)+(angleABD)+(angleDBE) = 180

(72)+(90)+(angleDBE) = 180

162+angleDBE = 180

angleDBE = 180-162

angleDBE = 18

We can also find this angle by noting that angles DBE and EBF add to 90.

So, (angleDBE)+(angleEBF) = 90 leads to angleDBE = 90-72 = 18

----------

Angles ABC and CBF form a straight angle as well

(angleABC) + (angleCBF) = 180

72 + angleCBF = 180

angleCBF = 180-72

angleCBF = 108