Chapter 5: Q11 (page 187)

Quad. is a rhombus.
If $m ∠ 1 = 25$ , find the measures of $∠ 2, ∠ 3, ∠ 4 and ∠ 5$ .

Short Answer

Expert verified

The measures of $∠ 2, ∠ 3, ∠ 4 and ∠ 5$ are $25 °, 65 °, 65 ° and 90 °$ respectively.

Step by step solution

Step 1. Property of rhombus.

The diagonals of a rhombus are perpendicular.

In quad. SLTM, LM and ST are diagonals of rhombus then by property of rhombus, $m ∠ 5 = 90 °$ .

Step 2. Description of step.

Diagonals of a rhombus bisects the vertex angles.

Here, $∠ L S M$ is divided into $∠ 1 and ∠ 2$ , that is, $m ∠ 1 = m ∠ 2$ . As $m ∠ 1 = 25$ , $m ∠ 2 = 25 °$ .

Step 3. Description of step.

Here, $∠ S L T$ is divided into $∠ 3 and ∠ 4$ , that is, $m ∠ 3 = m ∠ 4$ .

Step 4. Description of step.

Here, $∠ S$ and $∠ L$ are supplementary.

Substitute $m ∠ 3$ for $m ∠ 4$ .

$\begin{matrix} m ∠ 1 + m ∠ 2 + m ∠ 3 + m ∠ 4 = 180 \\ 25 + 25 + m ∠ 3 + m ∠ 3 = 180 \\ 2 m ∠ 3 = 180 - 50 \\ 2 m ∠ 3 = 130 \\ m ∠ 3 = 65 ° \end{matrix}$

Step 5. Description of step.

As $m ∠ 3 = 65 °$ and $m ∠ 3 = m ∠ 4$ implies that $m ∠ 4 = 65 °$ .

Therefore, the measures of $∠ 2, ∠ 3, ∠ 4 and ∠ 5$ are $25 °, 65 °, 65 ° and90 °$ respectively.

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Quad. is a rhombus.
If $m ∠ 1 = 25$ , find the measures of $∠ 2, ∠ 3, ∠ 4 and ∠ 5$ .

Short Answer

Step by step solution

Step 1. Property of rhombus.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Description of step.

Step 5. Description of step.

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Quad. is a rhombus.If m∠1=25, find the measures of ∠2,∠3,∠4and∠5.

Short Answer

Step by step solution

Step 1. Property of rhombus.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Description of step.

Step 5. Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Geometry

Applied Mathematics

Calculus

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Quad. is a rhombus.
If $m ∠ 1 = 25$ , find the measures of $∠ 2, ∠ 3, ∠ 4 and ∠ 5$ .