In the diagram shown, <1=<4 and<2=<3 The sum of the measures of the four angles is 140 The measure of <3 is 8 less than the measure of <4 What is the combined measure of angles 2, 3, and 4? A. 101° B. 107° C. 109° D. 117°

Question

Mathematics

Andrew

20 January, 14:14

In the diagram shown, <1=<4 and<2=<3 The sum of the measures of the four angles is 140 The measure of <3 is 8 less than the measure of <4 What is the combined measure of angles 2, 3, and 4? A. 101° B. 107° C. 109° D. 117°

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Nathanial · Answer 1

Ans is C. 109°

Set <2=<3 is x

because the measure of <3 is 8 less than the measure of <4, so <1=<4 is (x-8),

four angles is 140

(x-8) + (x-8) + x+x=140

4x-16=140

x=39°

the combined measure of angles 2, 3, and 4

39+39 + (39-8)

=109°