Supplementary angles are those whose measurements add up to 90 degrees True or False

Mathematics

2 answers:

erma4kov [3.2K]3 years ago

8 0

Answer: No

Step-by-step explanation:

Complementary means angles add up to 90 degrees.

Supplementary means angles add up to 180 degrees.

Since Supplementary doesn't add up to 180 degrees, the answer is false.

Papessa [141]3 years ago

4 0

Is false..... false

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Given: △ABC, AB=5 sqrt 2 m∠A=45°, m∠C=30° Find: BC and AC will give brainliest!!! By the way the answer is not 5 and 3.66

Makovka662 [10]

Answer:

Therefore,

$BC=a=10\ units\\\\AC=b=13.66\ units$

Step-by-step explanation:

Consider a Δ ABC with

m∠ A = 45°

m∠ C = 30°

AB = c = 5√2

To Find:

BC = a = ?

AC = c = ?

Solution:

Triangle sum property:

In a Triangle sum of the measures of all the angles of a triangle is 180°.

$\angle A+\angle B+\angle C=180\\\\45+30+\angle B=180\\\ttherefore m\angle B =180-75=105\°$

We know in a Triangle Sine Rule Says that,

In Δ ABC,

$\frac{a}{\sin A}= \frac{b}{\sin B}= \frac{c}{\sin C}$

substituting the given values we get

$\frac{a}{\sin 45}= \frac{b}{\sin 105}= \frac{5\sqrt{2} }{\sin 30}$

∴ $\frac{a}{\sin 45}= \frac{5\sqrt{2} }{\sin 30}\\\\a=\sin 45\times \frac{5\sqrt{2} }{\sin 30}\\\\a=\frac{1}{\sqrt{2} }\times \frac{5\sqrt{2} }{0.5} \\\\\\a=\frac{5}{0.5} =10\\\therefore BC = a = 10\ units$

Similarly for 'b',

$\frac{b}{\sin 105}= \frac{5\sqrt{2} }{\sin 30}\\\frac{b}{0.9659}= \frac{5\sqrt{2} }{0.5}\\\\b=0.9659\times \frac{5\sqrt{2} }{0.5}\\\\b=\frac{6.8301}{0.5} \\\\b=13.66\\\therefore AC = b =13.66\ units\\$