Answered

Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Get immediate and reliable solutions to your questions from a knowledgeable community of professionals on our platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

In the figure, angle D measures 71° and angle G measures 37°. What is the measurement of angle A?

Sagot :

cnfkcz5ccg

Answer:

34 °

Step-by-step explanation:

∠D = 71°

∠G = 37°

In ΔGEF

Using angle sum property of triangle : Sum of all angles of triangle is 180°

∠G+∠E+∠F = 180°

Since ΔGEF is right angled triangle at F so, ∠F = 90°

Now, 37°+∠E+90° = 180°

127°+∠E= 180°

∠E= 180°-127° =53°

Now ∠E+∠D = 53°+71°  = 124°

Now using exterior angle property in ΔABC

An exterior angle of a triangle is equal to the sum of the opposite interior angles

∠E+∠D is the exterior angle of  ΔABC

So, ∠A+∠B = ∠E+∠D

since  ΔABC is right angled triangle at B so, ∠B = 90°

∠A+90° = 124°

∠A = 124°-90°

∠A = 34°

Hence the measurement of angle A is 34 °

Assuming the following is a triangle, A = 72°

All interior angles of a triangle added together will always equal 180°, so [tex]180 - 71 - 37 = 72[/tex]

Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.