Determine Angle GDC: Complex Figure with 90° and 95° Known Angles

It is known that angles A and D are equal to 90 degrees

Angle DEB is equal to 95 degrees

Complete the value of angle GDC based on the data from the figure.

505050404040707070AAABBBCCCDDDEEEFFFGGG3025

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Step-by-step video solution

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00:00 Find angle GDC
00:11 The entire angle equals the sum of its parts
00:36 We'll substitute appropriate values according to the given data and solve for the angle
00:53 We'll isolate angle GDC
01:03 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

It is known that angles A and D are equal to 90 degrees

Angle DEB is equal to 95 degrees

Complete the value of angle GDC based on the data from the figure.

505050404040707070AAABBBCCCDDDEEEFFFGGG3025

2

Step-by-step solution

Note that the GDC angle is part of the EDC angle.

Therefore, we can write the following expression:

GDC+EDG=EDC GDC+EDG=EDC

Since we know that angle D equals 90 degrees, we will substitute the values in the formula:

GDC+40=90 GDC+40=90

We will simplify the expression and keep the appropriate sign:

GDC=9040 GDC=90-40

GDC=50 GDC=50

3

Final Answer

50

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Indicates which angle is greater

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