Triangle ABC is an isosceles triangle.
Solution:
Given data:
∠ABC = 70° and ∠ACD = 55°
<em>If two parallel lines are cut by a transversal, then alternate interior angles are congruent.</em>
m∠BAC = m∠ACD
m∠BAC = 55°
<em>Sum of the angles in a straight line add up to 180°.</em>
m∠ACD + m∠ACB + m∠ABC = 180°
55° + m∠ACB + 70° = 180°
m∠ACB + 125° = 180°
Subtract 125° from both sides, we get
m∠ACB = 55°
In triangle ABC,
∠BAC = 55° and ∠ACB = 55°
∠BAC = ∠ACB
Two angles in the triangle are equal.
Therefor triangle ABC is an isosceles triangle.
Write and solve an equation of ratios:
x 9
---- = ----
16 x
Cross mult., we get x^2 = (16)(9)
Taking the sqrt of both sides, we get x = plus or minus (4)(3), or
x= plus or minus 12
Since x is measure of distance here, omit the -12 result. x = +12 units
Answer:
Step-by-step explanation:
<u>The diameter is the hypotenuse of the triangle:</u>
- d = √8²+6² = √100 = 10 cm
<u>Area of the semicircle:</u>
- A = 1/2πr² = 1/2(3.14)(10/2)² = 39.25 cm²
<u>Area of the triangle:</u>
- A = 1/2bh = 1/2(6)(8) = 24 cm²
<u>Shaded area:</u>
<span>2n + 5 – (3n + 7) + 4n – 9
</span> <span>6n + 5 – (3n + 7) – 9
</span> <span>6n – 4 – (3n + 7)</span>
<span>6n – 4 – 3n – 7
</span> <span>3n – 4 – 7
</span> <span>3n –11</span>
Answer:
88 ft
Step-by-step explanation:
11ft times 8ft equals 88 ft. Its the same so the area is 88 ft.
