Question

Attachments included.

1. Find the missing angles.

2. The combined measurement of angles A,E, and K is 127 degrees. And angle G is 90 degrees. What is the measurement of B?

Answer 1

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Explanation:

Answer 2

(1) Answer: angles are 47, 51, 54 (for placement see description below)

Start with the bottom-right triangle. Use the fact that angles must add up to 180 degrees to determine the missing angle:

180=105+28+<x

<x = 47 degrees

Nest, the opposite crossing angle (marked with "?" is equal to x due to "opposite angles equality", let's call that <y=67 degrees

Next, we are in the top triangle where, again,

180 = 82 + <y + <z

180 = 82 + 47 + <z

<z = 51 degrees (this is the very top angle marked with "?")

Finally we are looking for the bottom-left angle marked with "?", let's call it <w.

There are multiple ways of determining <w, we will use the supplementary angle to the angle 105, which is 180-105=75 degrees, and the fact that we have a triangle with

180 = 75 + 51 + <w

<w = 54 degrees

So the missing angles are 47, 51, 54 (see placement above)

(2) Answer: 53 degrees (choice (C))

Steps:

Determine angle A as (combined measurement - 90 degrees) because E+K=90 degrees.

A = 127-90=37 degrees

then use

180 = A + B + C = 37 + B + 90

B = 53 degrees