Chapter 5: Q14 (page 187)

Quad. FLAT is a rectangle.
If $m ∠ 1 = 18$ find the measures of $∠ 2, ∠ 3$ and $∠ 4$ .

Short Answer

Expert verified

The measures of $∠ 2, ∠ 3$ and $∠ 4$ are $18, 72 and 72$ respectively.

Step by step solution

Step 1. Description of step.

The diagonals of the rectangle are equal in length and bisect each other.

Therefore, $O T = O A$ . As $O T = O A$ , by isosceles triangle theorem the angles opposite to these sides are equal, that is, $m ∠ 1 = m ∠ 2$ . Therefore $m ∠ 2 = 18$ .

Step 2. Description of step.

From the given figure it can be observed that $∠ 2$ and $∠ 3$ are complementary angles, such that,

$\begin{matrix} m ∠ 2 + m ∠ 3 = 90 \\ 18 + m ∠ 3 = 90 \\ m ∠ 3 = 90 - 18 \\ = 72 \end{matrix}$

Step 3. Description of step.

The diagonals of the rectangle are equal in length and bisect each other.

Therefore, $O A = O L$ . As $O A = O L$ , by isosceles triangle theorem the angles opposite to these sides are equal, that is, $m ∠ 3 = m ∠ 4$ . Therefore $m ∠ 4 = 72$ .

Therefore, the measures of $∠ 2, ∠ 3$ and $∠ 4$ are $18, 72 and72$ respectively.

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Quad. FLAT is a rectangle.
If $m ∠ 1 = 18$ find the measures of $∠ 2, ∠ 3$ and $∠ 4$ .

Short Answer

Step by step solution

Step 1. Description of step.

Step 2. Description of step.

Step 3. Description of step.

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Quad. FLAT is a rectangle.If m∠1=18find the measures of∠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.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Theoretical and Mathematical Physics

Geometry

Discrete Mathematics

Calculus

Decision Maths

Study anywhere. Anytime. Across all devices.

Quad. FLAT is a rectangle.
If $m ∠ 1 = 18$ find the measures of $∠ 2, ∠ 3$ and $∠ 4$ .