Advertisements
Advertisements
Question
In the following figure, ∆PQR is right-angled at P. U and T are the points on line QRF. If QP || ST and US || RP, find ∠S.
Advertisements
Solution
QP || ST and QT is a transversal.
∴ ∠PQT = ∠STQ ...[Alternate interior angles]
US || PR and UR is a transversal.
∴ ∠PRU = ∠SUR ...[Alternate interior angles]
Two angles of ∆PQR equal to two angles of ∆STU.
Therefore, the third angle also will be equal.
∴ ∠QPR = ∠TSU
Now, given that ∠P = 90°
∴ ∠S = 90°.
APPEARS IN
RELATED QUESTIONS
Using the measures of the angles given in the figure alongside, find the measures of the remaining three angles.
In ∆PQR, the measures of ∠P and ∠Q are equal and m∠PRQ = 70°. Find the measures of the following angles.
- m∠PRT
- m∠P
- m∠Q
Using the given figure find the value of x.
In the given figure find the value of x
In the figure find the value of x
In ∆ABC, ∠Α = 50°, ∠B = 70° and bisector of ∠C meets AB in D (see figure). Measure of ∠ADC is ______.
In the given figure, ∠UQR = ∠______ + ∠ ______
In the following figure, if RP = RQ, find the value of x.
What is the measure of an exterior angle if its adjacent interior angle measures 65∘?
A triangle has interior opposite angles measuring 50° and 75°. What is the measure of the exterior angle at the third vertex?
