Chapter 8: Q2. (page 287)

Use the diagram to complete each statement.
If $m ∠ R = k,$ then $m ∠ R S U = ?,$
$m ∠ T S U = ?,$ and $m ∠ T = ? .$

Short Answer

Expert verified

The final answer is $m ∠ R S U$ , \ $[m ∠ T S U \]$ and $m ∠ T$ are . $90 - k$ , $k$ and $90 - k$ .

Step by step solution

Step 1. Given information:

The right angles are shown below.

$m ∠ R = k$

Step 2. Concept used.

In a triangle the sum of angles is $180 °$ .

Step 3. applying the concept.

Now, we write the angles and their sum.

In triangle RSU,

$\begin{array}{l} m ∠ R S U + m ∠ R U S + m ∠ R = 180 (Sum of angles oftriangle) \\ m ∠ R S U + 90 + k = 180 \\ m ∠ R S U = 180 - 90 - k \\ m ∠ R S U = 90 - k \end{array}$

Angle $m ∠ T S U$ is calculated as follows:

$\begin{array}{l} m ∠ R S U + m ∠ T S U = 90 (Righttriangle Δ T R S) \\ 90 - k + m ∠ T S U = 90 \\ m ∠ T S U = k \end{array}$

Angle $m ∠ T$ is as follows:

$\begin{array}{l} m ∠ R S T + m ∠ R + m ∠ T = 180 (Sum of angles oftriangle) \\ 90 + k + m ∠ T = 180 \\ m ∠ T = 180 - 90 - k \\ m ∠ T = 90 - k \end{array}$

Therefore, the complete given statement is $m ∠ R S U$ , $m ∠ T S U$ and $m ∠ T$ are $90 - k$ , k and $90 - k .$

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Use the diagram to complete each statement.
If $m ∠ R = k,$ then $m ∠ R S U = ?,$
$m ∠ T S U = ?,$ and $m ∠ T = ? .$

Short Answer

Step by step solution

Step 1. Given information:

Step 2. Concept used.

Step 3. applying the concept.

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Use the diagram to complete each statement.If m∠R=k, then m∠RSU=?,m∠TSU=?, and m∠T=?.

Short Answer

Step by step solution

Step 1. Given information:

Step 2. Concept used.

Step 3. applying the concept.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Probability and Statistics

Geometry

Theoretical and Mathematical Physics

Decision Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Use the diagram to complete each statement.
If $m ∠ R = k,$ then $m ∠ R S U = ?,$
$m ∠ T S U = ?,$ and $m ∠ T = ? .$