Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

# How do I solve these questions? I'm not sure what to do.? Relevance

See below for work and solutions. • When angle c is 67°, angle d = 46°

When angle d is 38°, angle c = 71°

When angle e is 32°, angle f = 58°

When angle f is 36°, angle e = 36°

• for isosceles triangle the angles opposite the congruent sides are congruent

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For the problem on the left

When c is 67 the unmarked angle is also 67

Therefor

d = 180 - 67 - 67

d = 46º <––––

When d is 38

Each of the remaining angles are equal

180 - 38 = 142

c = 142/2

c  = 71º <––––––

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See image for the problem on the right

f = 52º <––––––

e= 36º <––––––– • One (of many) property of triangles: Angles add up to 180 degrees.

One property of isosceles triangles: two angles are equal (the ones at the end of both equal sides).

Therefore, the unmarked angle MUST be the same as angle c (67)

Add these two 67+67 = 134.

Whatever angle d is, must complete the sum of 180

d = 180 - 134 = ...

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If d=38, then the other two angles together must add up to 180-38 = 142

Since c and the "other angle" are equal, they each get half of that.

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Second triangle, first part:

First, consider the large triangle (hoping it is isosceles - not clearly indicated).

The sum must be 180

angle e is 32, leaving 180-32 = 148 for the other two.

If they are equal, then they must be each half of 148 = 74

(On the right side, this applies to the whole angle, not just the part marked f)

Now consider the smaller (bottom) triangle, clearly isosceles.

We now know that the bottom left is 74. This means that the "middle angle" on the left side must also be 74. This leaves 180-74-74 = 32

(in other words, if both the large triangle and the small one are isosceles, then f = e.

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second part, working backwards

if f = e, then clearly e=f.

You can build the reasoning using what you do for the first part... simply by going backwards.