Question

Find the measures of all the indicated angles in the picture. (Give letter statements before the numeric answer.) m∠FAJ = m∠EOK = m∠GBF = m∠CNM = m∠CDB = m∠OKL = m∠DCE = m∠BML = m∠JEI = m∠ALK =

Answer 1

Answer:

m∠FAJ = 75°

m∠EOK = 79°

m∠GBF = 64°

m∠CNM = 62°

m∠CDB = 37°

m∠OKL = 111°

m∠DCE = 25°

m∠BML = 82°

m∠JEI = 74°

m∠ALK = 68°

Step-by-step explanation:

Before starting to solve this question, let's remember some angle properties.

In any triangle, the sum of all its interior angles is equal to 180° (I)

In any pentagon, the sum of all its interior angles is equal to 540° (II)

A straight (flat) angle measures 180° (III)

A right angle measures 90° (IV)

When we have two lines (that have an intersection), the vertically opposite angles are equal. (V)

Angles on a straight line add up to 180°. (VI)

When we have two parallel lines that are intersect by a third line :

The corresponding angles are equal. (VII)

The alternate angles are equal. (VIII)

Remembering all this properties now we can follow up with the exercise.

Using (I), we can find the following angles :

m∠DOE = 101°

m∠AKE = 111°

m∠ALB = 112°

m∠BMC = 98°

Using (VI), we can find the following angles :

m∠DON = 79°

m∠EKO = 69°

m∠AKL = 69°

m∠ALK = 68°

m∠BLM = 68°

m∠BML = 82°

m∠EOK = 79°

m∠CMN = 82°

Using (V), we can find the following angles :

m∠KON = 101°

m∠OKL = 111°

m∠KLM = 112°

m∠LMN = 98°

Using (II), we can find that :

m∠MNO = 118°

Using (V) again :

m∠CND = 118°

Now in the point N, the sum of all 4 angles is 360° and also the vertically opposite angles are equal. Therefore, we find that

m∠DNO = 62°

m∠CNM = 62°

Using (I) we find that :

m∠LAK = 43°

Using (VI) we can find m∠FAJ which is :

m∠FAJ = 75°

Using (I) we find that :

m∠LBM = 30°

Using (VI) we find that :

m∠GBF = 64°

Using (I) we find that :

m∠KEO = 32°

Now using (VI) we find that :

m∠JEI = 74°

Using (I) we find that :

m∠ODN = 39°

Now using (VI) we find that :

m∠CDB = 37°

Finally, using (I) we can find that

m∠DCE = 25°

We have all the measures asked.