In the given figure- TQ and TR are bisectors of - Q and - R respectively- If - QPR -80- and - PRT -30- then- - TQR -A- 45-B- 25-C- 15-D- 35-

The correct option is D 35^∘ (i) ∠PQR=180^∘ (80^∘+30^∘)……Sum of ∠s of a Δ =180^∘ 110^∘ =70^∘ (ii) ∠PQT = ∠TQR = 70^∘/2…… (QT bisects∠PQR, given) =35^∘ ...

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Byju's Answer

Standard VII

Mathematics

Angle Sum Property of a Triangle

In the given ...

Question

In the given figure, TQ and TR are bisectors of $∠$ Q and $∠$ R respectively. If $∠$ QPR = $80^{\circ}$ and $∠$ PRT = $30^{\circ}$ , then, $∠$ TQR = ____.

$45^{\circ}$

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$15^{\circ}$

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$25^{\circ}$

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$35^{\circ}$

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Solution

The correct option is D
$35^{\circ}$

(i) $∠ PQR = 180^{\circ} - (80^{\circ} + 30^{\circ}) \dots \dots Sum of ∠ s of a Δ$

$= 180^{\circ} - 110^{\circ}$

$= 70^{\circ}$

(ii) $∠ PQT = ∠ TQR = \frac{70^{\circ}}{2} \dots \dots (QT bisects ∠ PQR, given)$

$= 35^{\circ}$

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In fig. TQ and TR are bisectors of $∠$ Q and $∠$ R respectively. If $∠$ QPR = $80^{\circ}$ and $∠$ PRT = $30^{\circ}$ . Determine $∠$ TQR. [4 MARKS]

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Q. In the given figure, AM ⊥ BC and AN is the bisector of ∠A. If ∠ABC = 70° and ∠ACB = 20°, then ∠MAN = ?
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Q. In the given figure, AB and CD are parallel lines and transversal EF intersects them at P and Q respectively. If ∠APR = 25°, ∠RQC = 30° and ∠CQF = 65°, then

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In the given figure, TQ and TR are bisectors of ∠Q and ∠R respectively. If ∠QPR = 80∘ and ∠PRT = 30∘, then, ∠TQR = ____.

The correct option is D 35∘ (i) ∠PQR=180∘−(80∘+30∘)……Sum of ∠s of a Δ =180∘−110∘ =70∘ (ii) ∠PQT=∠TQR=70∘2……(QT bisects∠PQR, given) =35∘

In the given figure, TQ and TR are bisectors of $∠$ Q and $∠$ R respectively. If $∠$ QPR = $80^{\circ}$ and $∠$ PRT = $30^{\circ}$ , then, $∠$ TQR = ____.

The correct option is D
$35^{\circ}$

(i) $∠ PQR = 180^{\circ} - (80^{\circ} + 30^{\circ}) \dots \dots Sum of ∠ s of a Δ$

$= 180^{\circ} - 110^{\circ}$

$= 70^{\circ}$

(ii) $∠ PQT = ∠ TQR = \frac{70^{\circ}}{2} \dots \dots (QT bisects ∠ PQR, given)$

$= 35^{\circ}$