Question 10 options: What is the measure of the third angle of the triangle?

Mathematics

1 answer:

Volgvan3 years ago

3 0

Answer:

83°

Step-by-step explanation:

The sum of all the angles in a triangle is 180°. This means that x + 44° + 53° = 180°. This can be simplified to x + 97° = 180°. To solve for x, we can subtract 97° from both sides (x = 180° - 97°) - this leaves us with x as 83°.

Hope this helps!

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Given line BD is congruent to BC, find the measure of angle B

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6x-9 = 3x+24
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x = 33/3
x = 11
Angle BCD:
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Angle BDC:
3×11+24 = 33+24 = 57°
Angle B:
x = 180° - 2×57°
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Answer:

1. SSS

2. Q and S

3. 20

Step-by-step explanation:

1. SSS similarity: If the corresponding sides of two triangles are proportional, then the two triangles are similar.

Triangles NLM and WUV are similar by SSS similarity, because

$\dfrac{NL}{WU}=\dfrac{36}{63}=\dfrac{4}{7}\\ \\\dfrac{LM}{UV}=\dfrac{40}{70}=\dfrac{4}{7}\\ \\\dfrac{NM}{WV}=\dfrac{24}{42}=\dfrac{4}{7}$

2. Completed steps:

a) draw a circle with center at P and radius r

b) draw a circle with center at Q and radius r

c) using compass, measure the distance between two points of intersection of the first circle with angle rays

d) using point of intersection of the second circle with PQ as a center, draw the circle of radius equal to the distance from c) to get point S

Last step: connect points Q and S, line QS will be parallel to line r.

3. If lines MN and UT are parallel, then angles MUT and VMN are congruent; also angles UTN and MNV are congruent.

AA similarity: In two triangles, if two pairs of corresponding angles are congruent, then the triangles are similar .

By AA similarity, triangles VMN and VUT are similar, thus

$\dfrac{VM}{VU}=\dfrac{VN}{VT}\\ \\\dfrac{VM}{VM+8}=\dfrac{49-14}{49}\\ \\49VM=35(VM+8)\\ \\49VM=35VM+280\\ \\49VM-35VM=280\\ \\14VM=280\\ \\VM=20\ units$