Chapter 5: Q17 (page 187)

$\bar{GM}$ is a median of right $Δ IRG$
If $m ∠ 1 = 32$ find the measures ofrole="math" localid="1637864336352" $∠ 2, ∠ 3$ and $∠ 4$ .

Short Answer

Expert verified

The measures of $∠ 2, ∠ 3 and ∠ 4$ are $32, 58 and 58$ respectively.

Step by step solution

Step 1. Description of step.

The length of the median is equal to half the length of the hypotenuse.

Therefore, $R M = G M$ .

Step 2. Description of step.

Consider $Δ R M G$ , in which $R M = G M$ then by isosceles triangle theorem, $m ∠ 1 = m ∠ 2 = 32$ .

Consider $Δ I R G$ such that

$\begin{matrix} m ∠ I G R = m ∠ 2 + m ∠ 3 \\ = 90 \end{matrix}$

Step 3. Description of step.

Consider $Δ I R G$ then by an angle sum theorem,

$\begin{matrix} m ∠ 1 + m ∠ 2 + m ∠ 3 + m ∠ 4 = 180 \\ 32 + (m ∠ 2 + m ∠ 3) + m ∠ 4 = 180 \\ 32 + 90 + m ∠ 4 = 180 \\ m ∠ 4 = 180 - 122 \\ = 58 \end{matrix}$

Step 4. Description of step.

Substitute 32 for $m ∠ 2$ into $m ∠ 2 + m ∠ 3 = 90$ to find the value of $m ∠ 3$ .

$\begin{matrix} m ∠ 2 + m ∠ 3 = 90 \\ 32 + m ∠ 3 = 90 \\ m ∠ 3 = 90 - 32 \\ = 58 \end{matrix}$

Therefore, the measures of $∠ 2, ∠ 3 and ∠ 4$ are $32, 58 and58$ respectively.

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$\bar{GM}$ is a median of right $Δ IRG$
If $m ∠ 1 = 32$ find the measures ofrole="math" localid="1637864336352" $∠ 2, ∠ 3$ and $∠ 4$ .

Short Answer

Step by step solution

Step 1. Description of step.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Description of step.

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GM¯is a median of right ΔIRGIf m∠1=32find the measures ofrole="math" localid="1637864336352" ∠2,∠3 and ∠4.

Short Answer

Step by step solution

Step 1. Description of step.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

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Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

$\bar{GM}$ is a median of right $Δ IRG$
If $m ∠ 1 = 32$ find the measures ofrole="math" localid="1637864336352" $∠ 2, ∠ 3$ and $∠ 4$ .