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Hoochie [10]
3 years ago
12

In ∆ABC, m∠ACB = 90°, m∠A = 40°, and D ∈ AB such that CD is perpendicular to side AB. Find m∠DBC and m∠BCD.

Mathematics
1 answer:
podryga [215]3 years ago
8 0

Answer:  ∠B = 50°

               ∠BCD = 40°

<u>Step-by-step explanation:</u>

ACB is a right triangle where ∠A = 40° and ∠C = 90°.

Use the Triangle Sum Theorem for ΔABC to find ∠B:

∠A + ∠B + ∠C = 180°

40° + ∠B + 90° = 180°

         ∠B + 130° = 180°

                  ∠B = 50°

BCD is a right triangle where ∠B = 50° and ∠D = 90°.

Use the Triangle Sum Theorem for ΔBCD to find ∠C:

∠B + ∠C + ∠D = 180°

50° + ∠C + 90° = 180°

         ∠C + 140° = 180°

                  ∠C = 40°

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The correct answer is the number in the note is 80 and the first digit is 8.

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The size of the angle QUP in the system formed by the <em>equilateral</em> triangle QUR, the <em>equilateral</em> triangle PUT and the square RUTS is equal to 150°.

<h3>How to determine a missing angle within a geometrical system</h3>

By Euclidean geometry we know that squares are quadrilaterals with four sides of <em>equal</em> length and four <em>right</em> angles and triangles are <em>equilateral</em> when its three sides have <em>equal</em> length and three angles with a measure of 60°. In addition, a complete revolution has a measure of 360°.

Finally, we must solve the following equation for the angle QUP:

<em>m∠QUR + m∠QUP + m∠PUT + m∠RUT =</em> 360

60 <em>+ m∠QUP +</em> 60 <em>+</em> 90 <em>= 360</em>

<em>m∠QUP +</em> 210 <em>=</em> 360

<em>m∠QUP =</em> 150

The size of the angle QUP in the system formed by the <em>equilateral</em> triangle QUR, the <em>equilateral</em> triangle PUT and the square RUTS is equal to 150°. \blacksquare

To learn more on quadrilaterals, we kindly invite to check this verified question: brainly.com/question/13805601

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